Uncertainty-based flood resiliency evaluation of wastewater treatment plants

Flood is one of the most devastating hazards, and often leads to excessive damage to people and infrastructures. The frequency and the magnitude of floods have increased over the last decades (Milly et al. 2002; Svensson et al. 2005; Smolka 2006; Goharian & Burian 2014; Zahmatkesh et al. 2014). Coastal flooding from tropical cyclones, sea level rise and hurricanes could affect many people in coastal regions that are prone to floods (Mousavi et al. 2011). Heavy rainfall, high tides, and human-based reasons such as inappropriate land use and increased population, as well as climate change impacts, can increase the potential for flooding (Nazif et al. 2012; Tingsanchali 2012; Karamouz et al. 2013; Goharian et al. 2015, 2016; York et al. 2015; Tavakol-Davani et al. 2016). There are numerous examples of devastating flood events that have led to considerable damage to communities. Examples are the floods that occurred in central Europe in 2002 and 2005, resulting in approximately 21.5 billion euros in financial damage (Kron 2005). The history of flooding in the United States also reveals that coastal areas, especially on the east coast of the USA, are highly vulnerable to floods and storms. The most recent flood events, hurricane Irene and super storm Sandy are evidence of extreme vulnerability.

Any damage to coastal cities’ infrastructures caused by flood hazard can paralyze the daily lives of people. Wastewater treatment plants are among the strategic infrastructures that make water usable for end users. Cities with combined sewer systems are more vulnerable in times of floods. This is due to the serious water pollution caused by combined sewer overflows; a situation in which both storm water and wastewater directly discharge to waterbodies and can cause adverse environmental and socio-economic impacts. Coastal cities and their infrastructures are becoming more prone to coastal flooding (Zahmatkesh et al. 2015). Gornitz et al. (2001) acknowledged that sea level rise and coastal erosion could make much of the New York City (NYC) coastline vulnerable to flood. Bowman et al. (2008) stated that because of the proximity of land to the mean sea level in NYC, hurricanes and tropical cyclones are capable of causing storm surge risks in much of the region. Considering the urbanized nature of NYC, there is added stress that flood risk threatens the natural and built environment because of the existence of critical infrastructure systems, their interdependencies and close relation with human settings.

The significant damage caused by recent floods in urban areas, such as NYC and New Orleans in the USA and European countries such as the Netherlands, indicates the need for change and review of the current understanding and methods of flood management. For this purpose, a holistic perspective that embraces various social, economic, and hydrologic features of the coastal system is needed. In previous studies, the change towards using non-structural means and measures in facing flood events can be observed. Anselmo et al. (1996) presented a coupling hydrological and hydraulic modeling approach for risk assessment of flood-prone areas. They applied their approach in analyzing the adverse impacts of flooding on thermoelectric power plants. Filatova et al. (2011) suggested different coastal management strategies to decrease potential damage, and as a result, reduce risk. They developed a conceptual model that links flood risk, the housing market, and individual risk awareness. Fu & Kapelan (2013) investigated the probabilistic dependence between rainfall depth and duration in flood risk analysis, which can play a vital role in flood risk management. Zheng et al. (2015) used a joint probability distribution of related factors in assessing flood risk in a coastal area.

Resiliency is a concept in flood disaster management describing the ability of a system to cope with flood, absorb the corresponding adverse impacts, and return to its normal condition (Simonovic & Peck 2013). Although there is no generally accepted meaning for resiliency, many agree that in defining it, some crucial characteristics are essential. Bruneau et al. (2003) were the first to give resilience a tangible meaning. They summarized resiliency in the 4Rs of robustness, redundancy, resourcefulness, and rapidity, that have been widely used by other researchers. Kendra & Wachtendorf (2003) used the concept of the 4Rs to examine the reconstruction of the Emergency Operation Center in NYC after its destruction in 2001. They proposed a method to highlight several aspects of resiliency. Their results showed that, despite the destruction of physical facilities, the organization established to manage crises in NYC could enable an effective response in terms of resiliency. Chang & Shinozuka (2004) defined a quantitative measure of resilience based on the earthquake loss estimation models for the Memphis water system in Tennessee. Considering multiple dimensions of resilience, such as technical, organizational, social, and economic, they proposed resilience measures that relate losses in future disasters to seismic performance. IPET (2009) mentioned that lack of resilience to overtopping expressly increased flooding for walls and structural components.

Cimellaro et al. (2010) proposed a framework for quantifying resilience using an analytical function. The proposed function considered the effect of earthquake as the disaster, the results of response and recovery, and effects of restoration and preparedness. They implemented this framework for evaluation of health care facilities subjected to earthquake in California. Zimmerman & Faris (2010) acknowledged that a deep understanding of the characteristics of critical infrastructure from the resiliency standpoint is necessary in creating future expectations and adaptation. Da Silva et al. (2012), using information and evidence from 10 cities, proposed a conceptual model based on resilient features to analyze urban systems in order to improve the adaptive capacity of urban populations. Simonovic & Peck (2013) presented a systems framework for quantification of resilience through system dynamic simulation. Five major factors, physical, economic, social, health, and organizational, were considered.

For quantifying resiliency, effective factors representing the system characteristics are required to be identified. Resiliency can be calculated by combining the identified factors considering their importance. Different methods based on multi-criteria decision-making (MCDM) techniques can be used for selection and ranking of the effective factors. MCDM has been used in many studies related to water resource management; for example, Raju & Duckstein (2004) used an integrated application of cluster analysis and MCDM by employing economic, environmental, and social criteria to rank water resource planning strategies in the Flumen Monegros irrigation area in Spain. Ronco et al. (2015) employed an MCDM approach to develop 300-year flood maps for several risk categories of human, cultural infrastructures, economic infrastructures, and environment in Switzerland.

There are uncertainties associated with data and model development, as well as utilizing engineering judgment (particularly when dealing with MCDM methods) to quantify performance criteria. As for flood resiliency, these uncertainties need to be quantified in order to determine the potential range of the resiliency's variation. Simonovic (2005) presented an algorithm, in which MCDM methods combined with fuzzy theory, to deal with uncertainty in water resource management. Moya et al. (2013) incorporated flood inundation uncertainties in modeling the hydraulics of the Timis–Bega basin in Romania. For this purpose, they used a cloud and cluster analyzing method. Their method was then compared with the Monte Carlo procedure in uncertainty analysis and showed the reduction of the time needed for uncertainty analysis. Alfonso et al. (2016) provided a method according to the concept of value of information (VOI) to investigate the use of uncertain information in decision-making and planning for floodplains. A VOI map, as the result, depicted floodplain regions in which additional information is required to assist spatial flood planning decision-making.

One recent example of MCDM techniques is the Preference Ranking Organization Method for Enrichment Evaluation (PROMETHEE) method. This method has preference in application due to its simplicity in comparison with other methods (Morais & de Almeida 2007). PROMETHEE was first introduced by Brans et al. (1984), and Brans & Vincke (1985), as a family of outranking methods for solving MCDM problems. These methods solve MCDM problems by comparing the preference relations among several alternatives to acquire information on the best alternative. Balali et al. (2014) compared the analytical hierarchy process (AHP) method with the PROMETHEE technique in selecting appropriate structural systems, and concluded that due to reasons such as its simplicity, ease of understanding, and consistency of results PROMETHEE is the preferred method. AHP, proposed by Saaty (1977, 1980), is a method used to model subjective decision-making processes based on multiple attributes in a hierarchical system (Tzeng & Huang 2011).

In this study, an approach is proposed and used to quantify the resiliency of wastewater treatment plants (WWTPs) as one of the most important services of urban systems. As a result, a better understanding of resiliency should be captured. By including hydro climatic phenomena such as surge followed by coastal flood and hurricanes, and also the loss of service due to the critical infrastructure interdependencies, this approach considers the vulnerability posed to WWTPs. Fourteen WWTPs are located in NYC. This city has experienced damaging storms of multiple proportions such as hurricane Irene and super storm Sandy. WWTPs in this cosmopolitan area have been exposed to such coastal flooding, which leads to deterioration in performance or even complete failure of these vital facilities. Hence, assessment of resiliency for this infrastructure could provide a framework to analyze and suggest how to strengthen them through physical and adaptive measures. To quantify resiliency, an index is proposed based on the four basic concepts of robustness, redundancy, resourcefulness, and rapidity. Robustness (Ro) is defined as the WWTP's intrinsic strength in facing floods without suffering considerable degradation or loss of functionality for providing a service to the public. Redundancy (Re) is the availability of alternative resources capable of satisfying the functional requirements of WWTPs in case of flood events. Resourcefulness (Rs) is the capacity to mobilize resources, prioritize, and identify problems. This factor is highly related to managerial skills to efficiently allocate financial and technological resources when flood occurs. Rapidity (Ra) is considered as the capacity of WWTPs to return to normal conditions in a timely manner.

WWTPs are compared based on the quantified values of resiliency, and their performance in dealing with flooding is investigated considering their characteristics as the factors used in development of the resiliency index. The AHP method is used for prioritizing the identified factors weighted by a group of experts. The developed method is based on the MCDM approach, and uses the weights and actual values of factors. Considering the uncertainties in determining the actual values of factors, the most appropriate probability distributions to those observed values of factors of more random nature are fitted. Consequently, the range of variation of resiliency for each WWTP is estimated. In addition, factors that can be strengthened by investment schemes are identified to improve resiliency.

The paper is organized as follows. The details of methodology are described in the next section. Then, a comprehensive analysis of the wastewater treatment plants in NYC is presented. Finally, the results are discussed followed by a summary and conclusion.

In order to develop the system's framework, the 4R criteria of resiliency are utilized. The proposed framework is a parametric approach based on the characteristics of the WWTPs that are effective on flood consequences. Therefore, at the first step, a list of quantifiable factors that are related to the performance and resiliency of WWTPs in times of flooding is prepared (Karamouz & Nazif 2013; Zahmatkesh 2014; Karamouz & Zahmatkesh 2016). These factors are from different data types, such as hydrological, social, economic, and technical. Then, actual values for the identified factors are collected. The considered factors (sub-criteria) are presented in Table 1. Based on the definition of the 4Rs of resiliency, it also determines partitioning resiliency into four different criteria, and which sub-criterion belongs to which criteria.

After determining the effective factors’ values, WWTPs’ characteristics (factors) are weighed based on their role and importance in the performance of the WWTP in dealing with floods. As a main step, it is determined which factor (as a sub-criterion) belongs to which resiliency term (i.e., Ra, Ro, Rs, and Rd) as the criterion. The 4Rs of resiliency are also weighted based on the assigned weights to sub-criteria and, along with the actual values and weights of the sub-criteria, are used to quantify WWTP resiliency. An index is developed for this purpose. A number of WWTPs are considered and then compared based on the quantified values of resiliency.

In order to characterize a WWTP and determine its resiliency, varieties of factors are identified and used (Table 1). To obtain the actual values for the factors presented in Table 1, different official reports including Bloomberg & Strickland (2013) and NYCDEP (2013) are used. In Table 1, factors with the potential to be improved by financial investment are also determined. These factors are used for further analysis.

On the surface, the criteria of robustness (Ro), redundancy (Re), resourcefulness (Rs), and rapidity (Ra) appear equally tied to quantify resiliency for an urban infrastructure such as a WWTP. However, the weight of these criteria could not be the same. Robustness and rapidity can be regarded as the ‘ends’ of resiliency. In other words, in order to describe the extent to which a WWTP is resilient, the criteria of both (Ro and Ra) must be fulfilled (i.e., these criteria could be considered as the final objectives for a resilient system). Robustness describes the strength of the WWTP and its ability to withstand a certain level of flooding without suffering degradation or loss of function of treatment of the wastewater. On the other hand, rapidity describes the ability of the system to meet goals and priorities in a timely manner in order to avoid disruption of service. Therefore, together, these two terms can represent the ends of resiliency for a WWTP. If the estimations of the WWTP's robustness and rapidity are both high, then it could be considered resilient. Moreover, redundancy and resourcefulness are means by which the system can become more resilient. These 4Rs are all terms of resiliency that should be taken into account when quantifying the resiliency of a system. Considering the text mentioned above, based on the system of interest, the importance (weight) of the 4Rs could be different.

Appropriating more resources and doing so in an efficient manner will increase the capacity of the system and, in turn, will also increase the resiliency. If the system is more resilient, then it will perform more closely in the way that was intended. In terms of the 4Rs, a WWTP is considered resilient if it can both manage the incoming raw wastewater load and also treat it to a particular quality level standard before discharging it as effluent.

Based on the main functions of WWTPs, in this study, weights for the four terms of resiliency are determined. If the resiliency of the infrastructure can be quantified, it would give stakeholders the opportunity to see a clearer picture of vulnerability. In addition, resources could be more efficiently allocated with the aim of increasing flood resiliency.

The relative importance (weight) of the factors is determined in the form of a questionnaire survey. For this purpose, a questionnaire was designed, and in order to get the best reliable information from the survey, experts were asked to complete it based on their engineering judgment. These experts were selected among a group of people that were well familiar with the concept of flood resiliency in WWTPs (including four professors, two practitioners, and one post-doctoral fellow). The experts were selected from different ages (30 to 65 years) and career lengths (10 to 30 years) as an indicator of their level of experience. The experience and the knowledge level of the experts were different. However, their understanding of the system's resilience against flooding was sufficiently adequate to be selected for this study. We could only locate a limited number of respondents due to the fairly new resiliency concept used in this study. We believe that the selected pool of respondents has provided answers from different perspectives. These answers are considered adequate to develop the methodology; however, a larger pool of respondents is needed for actual implementations. The questionnaire sample is similar to what is presented in Table 1, with an additional column to record the assigned weight by the expert (see Appendix, available with the online version of this paper). The weights assigned to each sub-criterion by different experts are combined to obtain a relative weight (w) for the sub-criteria. The weight of each sub-criterion indicates the overall importance of that to the flood resiliency of a WWTP. The higher the weight (e.g., a maximum of 10), the more important the sub-criterion is. The factors are compared on a scale of 1–10 where 1 and 10 indicate very low and very high importance, respectively.

For development of a resiliency index, actual values of WWTPs’ sub-criteria and their corresponding weights are used in a model developed utilizing the MCDM method. For this purpose, several governing equations (described later) are formulated. Based on the general concept of this method (where subjective information is used), resiliency could be quantified by summation of normalized weights times the normalized values of some factors. In the PROMETHEE approach, this general concept for more than one alternative (WWTP facility in this study) utilizes geometrical analysis to compare the values of each sub-criterion (factor) with the corresponding values for other alternatives to provide a better means of combining subjective (weights) and objective (value) data. The developed model uses the PROMETHEE method, which is based on MCDM. MCDM can be used to solve problems involving more than one alternative (different WWTPs in this study). MCDM problems typically consist of having to pick between a numbers of options. When given a set of alternatives, an MCDM framework can allow a more informed decision to be made. MCDM is particularly useful because a set of criteria may be inherently conflicting, and the best alternative may not be so readily obvious. Since criteria could be conflicting, and since a greater preference for one sub-criterion over another may be desired, MCDM requires assignment of a relative importance to each sub-criterion. For this purpose, pairwise comparison for every combination of sub-criteria to appropriately weight the criteria is used.

AHP method is used in order to determine the weights of the selected sub-criteria of the WWTPs based on the obtained information from the survey. AHP is an MCDM method that is based on pairwise comparison. This approach uses scaled numbers, expressing individual judgments, to reach preferences among the set of sub-criteria. In this method, pairwise judgments are based on the individual's knowledge and experience. Inconsistency of judgments in AHP is determined by calculating the inconsistency ratio. This ratio is used to capture the bias in allocating weights on different sub-criteria. It has been well described in the literature since being presented. Based on Saaty (1977), an inconsistency ratio of less than 0.10 is acceptable for evaluation purposes.

It should be noted that the resiliency of WWTPs is also obtained with a decision-making-based method using software called D-Sight (http://www.d-sight.com/). This software uses the PROMETHEE as a geometrical analysis for an interactive decision aid to combine subjective and objective data, and presents an approach for quantifying resiliency.

In order to increase WWTPs’ resiliency against flooding, financial resources can be allocated to improve relevant functions/factors. Since the resiliency index is calculated based on the estimated actual values, sub-criteria with financial investment potential to improve resiliency (indicated in Table 1) can be targeted. This is of particular use especially for WWTPs with low values of resiliency.

Various scenarios (presented in the Results section) are proposed and compared to assess how they can increase resiliency spending certain financial resources. For each scenario, the amount of money that is needed for increasing each economic-based sub-criterion for one unit is estimated based on the data sources. Then, the effect of increasing the actual values of the selected sub-criteria on improving resiliency is investigated. Increase in the actual values for multiple factors is also considered.

Values of resiliency that can be obtained from Equation (2) are based on initial estimated values of factors for WWTPs. Although these values are acquired based on the interpretation of the official reports, they could be subject to error and uncertainties arising from the method used for their determination. Therefore, there is uncertainty associated with data availability and accepting representative values of sub-criteria using engineering judgment, and also accepting minimum and maximum values of sub-criteria for WWTPs as the lowest and highest values. One of the important parts of this study is the determination of the variability of the estimated actual value of each sub-criterion. Monte-Carlo simulation is used in this study for uncertainty analysis.

Monte Carlo simulation is a numerical procedure to reproduce random variables that preserve the specified distributional properties (Tung & Yen 2006). In Monte Carlo simulation, the response of the system of interest is repeatedly measured under various system parameter sets generated from the known or assumed probabilistic distributions. It offers a practical approach for uncertainty analysis because the random behavior of the system response can be probabilistically duplicated. Therefore, each factor is assumed to be a random number with a certain distribution. This distribution can be estimated based on the observed values of that factor for all WWTPs. Not all of the sub-criteria could be treated as random numbers; therefore, a number of them are selected for this part of the analysis. By generating random numbers of selected sub-criteria actual values based on the determined distributions, the variation of resiliency for each WWTP could be obtained. This variation is useful for resiliency improvement, because it provides a range of variation from our initial estimates. Furthermore, it provides a framework for investigating how resiliency can be improved by improving the values of sub-criteria (depending on whether increasing or decreasing them is preferred).

The case study is NYC, which has experienced several storm events in recent years. Extratropical cyclone Sandy was a turning point. After this destructive super storm, some critical infrastructures of NYC, such as transit systems, were inundated and shut down for days, revealing the susceptibility of the megacity's infrastructure to coastal flooding (Kokoszka 2013). The Metro Hurricane Transportation Study (US Army Corps of Engineers 1995) describes some alarming issues about flood risk in NYC. For example, it was claimed that if a storm occurs it may produce surges of up to 30 feet above mean sea level in some parts of the city. Super storm Sandy shows a clear link between the risk caused by a hydro climate hazard and the load imposed on city infrastructure.

According to Figure 2, every part of the case study drainage area belongs to only one WWTP (it should be noted that this is a combined sewer system); therefore, there is no interrelation between plants.

In Table 2, actual values of the sub-criteria for different WWTPs are presented. In order to calculate the weights of each sub-criterion, the normalized weights of 17 sub-criteria are calculated using pairwise comparison through the AHP method. The weight of each criterion (i.e., 4Rs) is then calculated as the summation of all the corresponding sub-criteria weights. These weights are normalized so that the summation of the weights for the 4Rs criteria would be 1. In Table 3, the weights (relative importance) of sub-criteria and criteria are presented. These weights are obtained by post-processing the weights assigned to the factors by the experts.

Based on Figure 3, the most resilient treatment plants according to the proposed method are Wards Island, Jamaica, and North River. On the opposite side, the least resilient treatment plants are Rockaway, Hunts Point, and Oakwood Beach. This is in agreement in most parts by the report prepared by NYCDEP (2013). It is also observed that the resiliency results obtained by the proposed technique and based on the D-Sight method are similar.

By improving the actual values of sub-criteria through investment, the resiliency of WWTPs could be improved. Those sub-criteria with high weights (based on the ranking results) and low values (in comparison with the minimum and maximum historical values) are preferable for investment; because not only do they have more effect on the resiliency value due to their weights, they also have a great potential for improvement.

In order to incorporate the scheme proposed in the Methodology section, the following steps are taken:

• The sub-criteria that can act as random numbers or have an uncertain nature must be recognized. Among the considered factors, sub-criteria related to hydrologic features such as hurricane flood elevation, and sub-criteria that could have an effect on flood risk such as ‘percent of not at risk equipment (the percentage of equipment that is not at risk of flooding, for example, due to a high elevation or being water proofed)’ are considered as factors with an uncertain nature. Table 4 shows the complete list of the identified uncertain factors.

• The probability distribution functions for each sub-criterion's permissible values are obtained. This is done by examining different distributions such as normal, log normal, and Weibull, and then determining the best distribution function to fit to observed values of each sub-criterion for the 14 WWTPs. In Table 4, distribution functions and the corresponding parameters fitted to different sub-criteria are also presented.

• Based on the fitted distribution functions, 100 random values are generated for selected sub-criteria, and the resiliency values for 14 WWTPs are recalculated. The data generation yields 100 resiliency values for each WWTP.

As can be seen, the initial values of resiliency for some of the WWTPs, such as Jamaica and North river, are near the upper limit of the variation range. This shows that the recorded actual values of sub-criteria for these WWTPs were high relative to the maximum historical values observed for sub-criteria. Considering the values of sub-criteria (that are relatively high) for these WWTPs, their resiliency cannot be increased further because there is little room for improvement. On the contrary, WWTPs with initial resiliency value near the lower limit of the variation range, such as Newtown creek, Hunts point and Rockaway, have the potential for improvement. It also indicates that the recorded actual values for these WWTPs were underestimated in comparison to the other WWTPs. For these WWTPs, by increasing the actual values of the sub-criteria, there is some room for improving resiliency. It should be noted that the uncertainty analysis of weights is not performed in this study because it was not within the scope of this work and needs a relatively large number of experts for weighting factors. However, it is suggested that it be considered for extension of this study or for actual implementation of the methodology.

Based on the 100 generated values of resiliency for each WWTP, the most appropriate distributions are fitted to investigate the occurrence probability of resiliency values obtained for the WWTPs. The fitted distribution functions and statistics for the WWTPs are shown in Table 5.

It should be noted that the values of resiliency for the plants with high standard deviations (σ) are more uncertain than those with lower σs. Therefore, for example, estimated resiliency values for Bowery bay are less probable than those with lower standard deviations.

The WWTPs with low values of resiliency (near to the minimum value of the resiliency variation range as shown in Figure 4) are more important to be considered for allocation of financial resources. The cost of increasing economic-based sub-criteria for one unit of cost is shown in Table 6. The data in Table 5 are obtained from data sources such as the EPA (Environmental Protection Agency) and sites such as www.bls.gov, as well as engineering judgment and consultation with experts. The initial analysis of the results shows that at least a 30% increase in the actual values is required for improvement of resiliency. It should be noted that in estimating the effect of financial investment on the ‘Percent of not at risk equipment in each WWTP’, shown as factor Ro₄, in the absence of any related data it is assumed that 20% of at risk equipment falls into the electrical category that can be placed at a higher elevation, and its submergence capability enhanced. Based on this assumption, improvement in Ro₄ can be as much as 30%.

Table 7 provides the descriptions of six defined scenarios. Based on the results provided in Figure 4, the effect of implementing these scenarios to improve the resiliency of Rockaway, as an example which has the lowest resiliency value among the considered WWTPs, is investigated.

As can be seen in Table 7, scenario numbers 1, 6, and 7 require an extremely high cost value compared to the others, which makes these options impractical. The high cost of structural expansion is the main reason for the high cost of these scenarios. Considering the results presented in Table 6, it can be concluded that, in general, structural measures are expensive to implement and cannot considerably improve the resiliency. However, non-structural measures, such as increasing plant staff, are cost-effective and consequently are preferred for use. In terms of recovery from flooding, the return to normal plant operations can be attributed to the plant staff when they try to reduce the amount of damage to critical equipment. According to NYCDEP (2013), plant staff could undertake many precautionary tasks, such as sandbagging low-lying buildings, relocating some of the portable equipment, filling chemical tanks, making sure that emergency power equipment is operational, and shutting down certain inflow pipes to reduce the inflow of combined sewage to the plant. By comparing scenarios regarding the percent of increase in the resiliency and the estimated costs, scenarios 2 and 3 present better improvement; however, after consultation with experts, the effect of plant staff on resiliency seems to be overestimated in these scenarios. Therefore, scenario 5 can be considered as the best alternative.

In this study, a framework is proposed to quantify the resiliency of WWTPs as key urban infrastructures in coastal areas. For this purpose, 14 WWTPs in NYC are considered. The WWTPs are characterized based on factors that are used in quantifying resiliency. These factors are weighted using experts’ opinions and the AHP method. Actual values of factors are also obtained from different resources. To utilize actual values and weights of factors for quantifying resiliency, a model is developed in MATLAB software based on the MCDM method. The factors are ranked and resiliency is quantified based on the four terms of robustness, rapidity, resourcefulness, and redundancy.

WWTPs are compared considering the obtained values for resiliency. Based on the results, the most effective factors are determined. An uncertainty based method is used to determine the range of variability of factors with random elements and to see how these factors could be strengthened to improve resiliency. An example demonstrates how financial resources could be allocated to strengthen the factors attributed to resiliency. Different scenarios are defined to present alternatives for investment to improve resiliency. The cost of implementing the proposed scenarios and the percent of increase in the resiliency is then calculated, and the best scenarios are identified.

Results show that, based on the proposed algorithm for WWTPs, rapidity (Ra) has the maximum effect on resiliency in comparison to the other resiliency terms (i.e., Re, Ro, and Rs). Investigating uncertain factors shows that resiliency has the potential to be improved by variation of some factors. Analysis of the results also shows that investment in non-structural measures is substantially more cost-effective than in structural measures such as expanding the plant capacity. An increase in the number of plant staff could also affect post-stress recovery (Ra₄). The plant staff could accelerate the system's recovery by working before, during, and after a hurricane. The results have demonstrated how partitioning resiliency into several criteria with different sub-criteria, determining the values of those sub-criteria and assigning weights to them, as well as incorporating uncertainties in the flood resiliency analysis, can assist in providing an initial assessment of the required capital investment for a system's preparedness to face flood hazard and disaster.

The proposed methodology is based on a value–weight linear relationship. This simplified assumption made quantification of resiliency easy and possible based on the available data and information. However, complex parametric methods can be proposed and applied for resiliency assessment. For this purpose, studies should be performed on the possible relations between different components (values and weights of different factors) of the method. As for uncertainty analysis, a larger group of respondents may be needed to develop probability distribution functions on the weights of factors and to incorporate this uncertainty into the analysis. Moreover, optimization algorithms can be formulated to determine how a certain amount of budget can be allocated to improve resiliency.