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Available online at www.sciencedirect.com

ScienceDirect journal homepage: www.elsevier.com/locate/watres

Valuing flexibilities in the design of urban water management systems Yinghan Deng a, Michel-Alexandre Cardin a,*, Vladan Babovic b,c, Deepak Santhanakrishnan a, Petra Schmitter b, Ali Meshgi b a

Department of Industrial and Systems Engineering, National University of Singapore, Block E1A #06-25, 1 Engineering Drive 2, Singapore 117576, Singapore b Singapore-Delft Water Alliance, Block E1 #08-25, 1 Engineering Drive 2, Singapore 117576, Singapore c Department of Civil & Environmental Engineering, National University of Singapore, Block E1A, #07-03, 1 Engineering Drive 2, Singapore 117576, Singapore

article info

abstract

Article history:

Climate change and rapid urbanization requires decision-makers to develop a long-term

Received 8 April 2013

forward assessment on sustainable urban water management projects. This is further

Received in revised form

complicated by the difficulties of assessing sustainable designs and various design sce-

4 September 2013

narios from an economic standpoint. A conventional valuation approach for urban water

Accepted 10 September 2013

management projects, like Discounted Cash Flow (DCF) analysis, fails to incorporate un-

Available online 23 October 2013

certainties, such as amount of rainfall, unit cost of water, and other uncertainties associated with future changes in technological domains. Such approach also fails to include the

Keywords:

value of flexibility, which enables managers to adapt and reconfigure systems over time as

Urban water management systems

uncertainty unfolds.

Real options analysis

This work describes an integrated framework to value investments in urban water

Engineering system design and

management systems under uncertainty. It also extends the conventional DCF analysis

evaluation

through explicit considerations of flexibility in systems design and management. The approach incorporates flexibility as intelligent decision-making mechanisms that enable systems to avoid future downside risks and increase opportunities for upside gains over a range of possible futures. A water catchment area in Singapore was chosen to assess the value of a flexible extension of standard drainage canals and a flexible deployment of a novel water catchment technology based on green roofs and porous pavements. Results show that integrating uncertainty and flexibility explicitly into the decision-making process can reduce initial capital expenditure, improve value for investment, and enable decision-makers to learn more about system requirements during the lifetime of the project. ª 2013 Elsevier Ltd. All rights reserved.

* Corresponding author. Tel.: þ65 6516 5387. E-mail address: [email protected] (M.-A. Cardin). 0043-1354/$ e see front matter ª 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.watres.2013.09.064

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1.

Introduction

Traditional water resources planning and analysis methods are based on requirements that are unrealistically deterministic (Medellı´n-Azuara et al., 2007). Under such considerations, the most common practice consists of three phases. First, after relevant data is collected and analyzed, the most likely scenarios are identified, which include projections of major exogenous drivers of the system, such as markets, government policy, and climate change. Then, according to those predictions, system designers generate design concepts and select design parameters that enable the system to perform optimally under the predictions. Economic evaluation of the design is then conducted, of which standard methodology, like discounted cash flow (DCF) analysis, optimization, and scenario planning, is applied to achieve the best optimal design (de Neufville & Scholtes, 2011). Such kind of design practice based on deterministic forecasts and the assumption of fixed design parameters, however, may not provide a design that performs best in the real world. First, the typical approach does not capture the sociotechnical and economic uncertainties that affect the water resources systems, which ultimately shapes the efficacy of water supply systems (Zhang & Babovic, 2011) e e.g. markets, regulations, and technology. Such system as designed to be optimal in a specific realization of the future achieves the expected performance only when the predicted scenario is realized. Besides, standard design and evaluation analysis, which uses expected values as inputs, may also mislead decision-makers, and lead to incorrect design decisions (de Neufville & Scholtes, 2011). This is because the output response (e.g. economic value, rainfall drainage or storage) of most complex systems today is not linear, and the performance observed in downside scenarios cannot be balanced by the upside scenarios. Such situation is described as “flaw of averages” (Savage, 2000). Furthermore, the conventional approach of DCF is not able to capture managerial flexibility (Trigeorgis, 1996). The sequence of decisions is embedded over time in the cash flow profile as irreversible investment at t ¼ 0. The system is assumed to remain “passive” and even though in reality managers would try and adapt to the environment so as to capture better economic performance. Standard DCF does not account for such flexibility which may consequently leads to an underestimation of the performance of systems and veils the ability of systems in managing uncertainties. Due to the reasoning above, a paradigm shift in systems design and evaluation is in need. Flexibility in engineering design is one avenue to deal with uncertainty pro-actively. In this case, flexibility e also referred as real options e is defined as the “right, but not the obligation, to change a project in the face of uncertainty”(Trigeorgis, 1996). This different perspective on systems design and evaluation is characterized by considering a wide range of possible future scenarios and taking pro-active actions to mitigate critical uncertainty sources. There are several applications of this methodology on large-scale infrastructure systems (Babajide et al., 2009; Buurman et al., 2009; Cardin et al., 2008; Michailidis et al., 2009), which have demonstrated that incorporating flexibility considerably improves the life cycle

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performance of systems. One typical example of flexible engineering designs in the real estate sector is the Health Care Service Corporation (HCSC) building in Chicago. In 1997, the building was initially designed to prepare for expansion if demand for working space reached a certain level in the future. The second phase of the vertical expansion option was exercised in 2010 (Guma et al., 2009). The rest of this paper is organized as follows. The next section discusses the motivations to apply the aforementioned approach, which considers explicitly uncertainty and flexibility, to designing and evaluating urban water management systems. The relevant literature is reviewed, and the research gap for further contribution is identified. Following this section, the details of the proposed methodology in this paper are introduced. Then a case study on a novel water infrastructure system is presented, as to demonstrate the implementation of the proposed methodology as well as its effectiveness in terms of improving performance of the target system. Finally discussions and conclusions are made in the last section.

2.

Motivation

The world is experiencing a high rate of urbanization. For those countries with highly urbanized population, like Singapore (100% of total population in 2010), the size of urban population is still growing; while for countries which are not highly urbanized at the current stage, like China (47% of total population in 2010), the rate of urbanization change is high (Urbanization, 2012). Increasing urbanization worldwide could intensify local competition for all types of resources, water being amongst the most vital (Zoppou, 2001). In addition, many other factors, like land scarcity, climate change, and depleting energy resources, require urban system designers to think forward and provide efficient solutions that make better use of resources and maintain sustainability. Development of sustainable water systems has been subjected to heated discussions recently. These systems are defined as “water systems that are managed to satisfy changing demands placed on them (both human and environmental) now and into the future, whilst maintaining ecological and environmental integrity of water” (UNESCO, 1998). However, for such emerging sustainable urban water management systems, we lack knowledge of how sustainable development should be attained and how sustainability of various technical systems should be assessed (Hellstrom et al., 2000). Traditional water resources planning and analysis methods based on fixed requirements and design parameters do not address how to properly evaluate systems under uncertainties as well as how to effectively manage uncertainties that are pervasive in urban systems of today. Some studies have been proposed to support the decision process to manage urban water (Makropoulos et al., 2008; Pearson et al., 2009; Thomas and Durham, 2003). Results from these studies provide suggestions and tools on selection of design alternatives and making policies. For example, Integrated Water Resource Management (IWRM) is proposed to support the management of alternative water resources from multiple perspectives (Thomas and Durham, 2003). Those

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studies, however, have not explicitly accounted for the various sources of uncertainties, like instability of technical efficiency or fluctuation in rainfall that may impact the results of decision-making. Some of the recent studies have taken one step further to recognize the exogenous and endogenous uncertainties faced by water systems, and even explicitly take those uncertainties into account when doing evaluation analysis. For example, Morimoto and Hope (2001, 2002) applied probabilistic techniques to the cost-benefit analysis of hydroelectric projects in Sri Lanka, Malaysia, Nepal, and Turkey, where they generated Net Present Value (NPV) distribution for design alternatives. Their analysis, however, has not incorporate pro-active actions to handle situations that may go beyond designers’ predictions. Even though sensitivity analysis is conducted, it merely acts as one part of the evaluation process and not as a way of inspiring novel solutions to optimize the design itself. In some studies (Pahl-Wostl et al., 2007), Adaptive Management is introduced into urban water management. These works, however, mainly deal with the operational part of the systems and have not revealed how to make changes to design configurations of the system as well as how to measure the additional benefits brought by those changes. In light of the situation explained above, this study considers applying flexibility in engineering design thinking to planning and assessment of urban water management systems. It has been indicated that incorporating flexibility into systems can bring about performance improvements ranging between 10% and 30%, compared to standard design and evaluation approaches (de Neufville and Scholtes, 2011). These improvements are achieved because flexible designs enable systems to hedge against downside scenarios (e.g. by reducing the scale of initial capital expenditure) and prepare for the unexpected favorable conditions (e.g. by allowing for future expansion of the system). For example, in the case of Iridium and Globalstar, the company would be able to reduce the life cycle cost by more than 20% if a phasing deployment strategy could have been adopted (de Weck et al., 2004). A set of procedures has been proposed in terms of designing and evaluating flexibility in complex engineering systems (Cardin et al., 2007, 2008; Zhang & Babovic, 2011). One such procedure (Cardin et al., 2007) starts with conventional design and evaluation approaches, and then further investigates into uncertainty and flexibility of the target system. Although the detailed modeling of each system and its specific flexibility varies from system to system, it is expected that those procedures and frameworks can be modified and applied in the context of urban water management systems. Indeed, there were some recent studies already moving toward this direction by using the real options approach to analyzing water systems. For example, Zhang and Babovic (2012) have conducted real options analysis to identify optimal water supply strategies, and Wang (2005) applied the approach to optimize the development of a hypothetical river basin involving decisions to build dams and hydropower stations. These studies have indicated that by applying flexibility analysis to water systems, designers are able to offer more cost-effective and sustainable solutions. The main contribution of this paper is a systematic methodology to analyze urban water management systems in an

engineering context, considering uncertainty and flexibility explicitly as part of the engineering design and management process. The methodology is similar to the approaches used by Zhang and Babovic (2012). However their work is mainly focused on strategic policy making, while the methodology introduced in this paper is rooted in an engineering design perspective. As for Wang’s (2005) study, the logic of doing the analysis is similar, but the target system of Wang’s study is hydroelectric dams, which differ with urban water management systems in terms of scale and complexity. Besides, the uncertainties faced by these two kinds of water systems are also distinct. Different modeling techniques need to be proposed so as to simulate the behavior of the system and its uncertainty drivers in an urban context. Furthermore, Wang applied mixed integer programming to modeling the decision-making process and relied on dynamic programming in the aspect of evaluation. This approach, however, imposes limitation on the decision rules being evaluated, and may be trapped by curse of dimensionality when confronted with a multitude of decision periods and states. The approach here incorporates decision rules as another variable in the analytical model, which enables modeling of diverse decision rules with relatively less computational burden. Besides, it is a direct extension of existing design and evaluation approaches, and is designed via a systematic step-wise process for more practical impact in engineering practice. Another contribution from a modeling standpoint involves the use of so-called Intensity Duration Frequency (IDF) curves to simulate the rainfall behavior in order to understand how rainfall intensities and durations as uncertainty factors may influence the economic performance of the system. The last contribution is to report on the first application of this methodology in the design and deployment of porous pavement and green roof technologies, as a way to recuperate and store grey water from natural rain events. Since not many studies have been done, the study provides another example of how these ideas can be considered in urban water management systems and how this new catchment technology can be better deployed. It is hoped that the results reported here will offer a different perspective on how to design, evaluate and implement urban water management systems, which can be of value to both research scholars and practitioners.

3.

Methodology

This study proposes a four-step procedure to design and evaluate flexible urban water management systems. The procedure is based on and modified from a design process proposed by a past study (Cardin et al., 2007). Similar to the original one, this proposed methodology is also a step-wise process on flexibility in design and evaluation, starting with the baseline model and further stepping into the uncertainty analysis and the flexibility analysis. One additional step of sensitivity analysis is added as to provide more reliable analytical results.

3.1.

Step 1: Baseline model

The starting point of the methodology is to build a baseline model. The objective here is to understand the main

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components of the system that influence its full life cycle performance. Costs and benefits involved in the system are calibrated by defining necessary design parameters and design variables. Additionally, assumptions on the system are defined. Following that, a preliminary deterministic costbenefit analysis (Boardman et al., 2006) can be carried out. Generally, in this step, the conventional DCF model is built to assess the performance of the system under the deterministic conditions. This step captures the standard practice in terms of design and project evaluation.

3.2.

Step 2: Uncertainty analysis

In this step, designers need to model major uncertainty drivers, and investigate design alternatives under a range of possible future scenarios. Historical data on the uncertainty drivers is collected and calibrated into stochastic or probability models, like Geometric Brownian Motion (GBM) and normal distribution. Then simulation is applied to generate scenarios that are used to assess the life cycle performance of design alternatives. The performance of these designs is compared under the criteria of Expected Net Present Value (ENPV), VAG (Value At Gain, which quantifies the performance in the upside scenarios), VAR (Value At Risk, which quantifies the performance in the downside scenarios), and variance. Through this analysis, designers capture a more comprehensive picture about the pros and cons of the design alternatives, compared with the deterministic analysis in Step 1.

3.3.

Step 3: Flexibility analysis

In this step, designers first need to generate flexible design concepts. A complete flexible concept is defined by four elements: uncertainty source, flexible strategy, flexible enabler, and decision rule (Cardin et al., 2013). Flexible strategies are the actions designers can take when a particular path of uncertainties is realized (e.g. expand the capacity of the system if demand turns out to be higher than prediction), while flexible enablers are the design configurations that make the strategies feasible from a design and management standpoint. A decision rule is a triggering mechanism or an “if” statement that specifies clearly when the flexible strategies will be exercised, based on some uncertainty realizations. For example, in the case of the HCSC building (Guma et al., 2009), the flexible concept can be “in order to deal with the uncertainty from working space demand, extra strength is added into the load bearing walls so that the building can be expanded if the working space is not enough”. In this case, adding extra strength is the flexible enabler and capacity expansion is the flexible strategy, while the “if” statement about the working space is the decision rule. After flexible concepts are generated, they are evaluated under the same scenarios and metrics stated in Step 2. The Value of Flexibility (VoF) is calculated by Equation (1). VoF ¼ ENPVflexible design  ENPVbaseline design

(1)

The computation of VoF can be resolved from several perspectives. The classical works in pricing financial options (Black and Scholes, 1973; Cox et al., 1979) are the origins of the

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valuation of real options. Later, the binomial approach proposed by Cox et al. (1979) was suggested to value options on real investments, hence real options (Trigeorgis, 1996). This approach has also been applied to obtaining the value of real options in engineering systems (de Weck et al., 2004). Decision tree is another method to assess the VoF, when the number of decisions is limited and the uncertainty can be modeled by discrete random variables. This method has been adopted to evaluate the VoF in oil deployment projects (Babajide et al., 2009). An important aspect of these two methodologies is that the evaluation process relies on dynamic programming where the decision rule essentially is decided by optimizing at each decision point based on expected value. This kind of approach may not capture well the full realm of possible decision rules. Besides, as the number of decision-making periods and states increases, the computation may become intractable. Although the assumption of path-independency in the binomial approach allows a recombination structure to reduce computational burden, this assumption of pathindependency may not hold for engineering systems. This is because different realizations of uncertainty may lead to different changes on system configurations which in return result in different realizations in the next time period (e.g. upgrading the efficiency of urban water systems may lead to lower price of water next period). Another approach to obtain the VoF is simulation. This approach can be more generally applied, since it has fewer restrictions on the number of time periods being considered and the distribution of uncertainties. Besides, this approach considers decision rules as explicit variables in the modeling framework, so that the model itself can be more easily modified to capture more diverse design configurations.

3.4.

Step 4: Sensitivity analysis

Finally, sensitivity analysis is carried out in order to assess how the results obtained following the above steps respond to changes in underlying assumptions. This step can be seen as a way to test the robustness of the design alternatives in response to the variation that may happen to the assumptions. There are several standard mathematical methods that can be applied in terms of doing sensitivity analysis. For example, one-factor-at-a-time method (OFAT) (Czitrom, 1999) is one of simplest and most common approaches.

4.

Application

In order to demonstrate an application of the methodology introduced above, this study applies the approach to the feasibility analysis of a new water technology. Besides, the results from this section also work as a demonstration to show that the methodology is effective in terms of improving the performance of urban water management systems.

4.1.

Problem definition

As part of an effort to investigate possible solutions for nextgeneration water infrastructure systems, which aim to reduce damage caused by floods in rainy seasons and re-use of

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Table 1 e Assumptions on parameters and input data. Assumptions and Input Data Catchment area (m2) Recycle efficiency (roofs)

82,000 0.45

Existing area of canals (m2)

2600

Depth (pavements) (m) Depth (space underneath of roofs) (m) Maintenance cost (pavements) ($/m2) Water price ($/m3)

0.3 0.3 1.0 1.7

Average No. of rain events (year)

178

Expansion cost (pavements) ($/112.5 m3)

70,000

Pave area (m2) Recycle efficiency (pavements) Expanded area of canals (m2) Porosity (roofs) CAPEX (design A) ($)

7500 0.65

Roofs area (m2) Depth of canals (m)

13,000 0.5

5400

Porosity (pavements)

0.3

0.6 150,000

Depth (vegetation of roofs) (m) CAPEX (design B) ($)

0.15 421,875

Maintenance cost (roofs) ($/m2) Water treatment cost ($/m3) Average rainfall in one rain (mm) Expansion cost (roofs) ($/650m3)

1.2

Maintenance cost (canals) ($/m2)

0.85

0.3

Flood damage cost ($/m3)

0.5

13.16

CAPEX (Flexible B) ($)

300,000

50,000

Expansion cost (canals) ($/740 m3)

48,000

the run-offs, a new technology based on porous pavements and green roofs is being proposed. The technology allows rainwater to infiltrate into the sub-surface layer where it is temporarily stored. For porous pavements, the sub-surface layer is filled with porous materials, while for the green roofs, the vegetation cover and space underneath function as the storage facility. The stored rainwater is then either detained in the ground, or be harvested by the pipe installed under pavements or the underneath space of green roofs. Later this harvested water can be recycled as “grey” water or be channeled to reservoirs. By implementing this technology, revenues (as cost savings of re-using rainwater) are generated. Besides, the porous pavements and green roofs reduce frequency and peak flow rate of rainwater that enters the drainage system. Consequently, less space is required for drainage, and the likelihood of flooding damage is also reduced (Zhang and Buurman, 2010). A test site has been chosen for a preliminary analysis on the possibilities and limitations of this innovative solution. The site is located within the Kent Ridge campus of the National University of Singapore (NUS). The size of the catchment has an area of about 8.2 ha. The land use distribution of the catchment comprises the following: 41% of bushes, 35.5% of other green areas, mostly grass patches on mild and steep slopes, 16.8% of rooftop and 4.77% of road areas. There are two considered design alternatives: a traditional expansion of the current drainage canal system (referred as design A) and alternative based on catchment measures of porous pavements and green roofs (referred as design B). Although design B has several aforementioned advantages compared with design A, since design B incurs a higher construction cost and maintenance cost, analysis is needed to better understand the costs and benefits. Also, one aims to assess whether there is potential to further improve the

Table 2 e Results of deterministic analysis.

NPV ($)

Design A

Design B

Best Design

266,846

252,274

Design B

economic performance of those two design alternatives under uncertainties by applying the flexibility analysis.

4.2.

Step 1: Baseline DCF model

The following is the list of notations used in the analysis. Areatotal total area of the test site under study (m2) area that can be deployed to porous pavements (m2) Areap area that can be deployed to green roofs (m2) Arear drainage capacity of canals in design A (m3) DCA drainage capacity of canals in design B (m3) DCB depth of canals (m) Dc area of existing canals (m2) Areac area of expanded canals in design A (m2) AExpc storage capacity of porous pavements (m3) SCp SCr storage capacity of green roofs (m3) depth of porous materials in porous pavements (m) Dp depth of vegetation covers in green roofs (m) Drc depth of underneath space in green roofs (m) Drs porosity of porous materials in porous pavements Pp porosity of vegetation covers in green roofs Pr recycle efficiency of porous pavements Rep recycle efficiency of green roofs Rer CAPEXA initial investment of design A ($) CAPEXB initial investment of design B ($) Uf unit flood damage cost ($/m3) UmA unit maintenance cost of design A ($/m2) unit maintenance cost of porous pavements ($/m2) Ump unit maintenance cost of green roofs ($/m2) Umr Uc unit cost of water treatment ($/m3) dr discounted rate annual cost in kth year ($) ACk annual revenue in kth year ($) ARk unit water price in kth year ($/m3) Prk rainfall quantity of the ith rain of the kth year (m) RQik number of rain events of the kth year RNk The assumptions for the design parameters and input data needed in the case study are shown in Table 1. The cost information is based on personal communications with the

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Fig. 1 e 2000 scenarios of annual unit water price.

design team members (as shown in Table 1). Although it may not be perfectly accurate, it is based on experienced designers’ inputs and reflects the essence of the system to some degree. The annual rainfall information is summarized from the online published data of National Environmental Agency (Weather Statistics, 2013). For design A, the following equations are developed. As there are no mechanisms of generating revenues, the analysis

only needs to quantify the costs involved. There are two categories of costs under consideration. Flood damage cost is calculated based on the occurrence of the rain events where the rainfall quantity exceeds the drainage capacity. Maintenance cost is a variable cost that links with the drainage area. The maintenance cost is related to activities of physical cleansing, maintenance and minor structural repairs of drains and canals.

Fig. 2 e Procedures of generating rainfall scenarios.

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ACk ¼

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RNk X

4.3.

 maxð0; RQ ik  Areatotal  DCA Þ  Uf þ Areac

i¼1

 þ AExpc UmA

(2)

  DCA ¼ Areac þ AExpc  Dc

NPVA ¼ CAPEXA 

50 X

(3)

ACk k

k¼1 ð1 þ drÞ

(4)

As to design B, more refined equations are developed, since not only costs need to be quantified but also the revenues generated as cost savings. In this case, the extra rainwater, that can neither be evacuated through drainage canals nor be captured by the new catchment measures, incurs flood damage cost. For the existing drainage canals, the maintenance cost is estimated by the same approach with design A. For porous pavements, the maintenance cost is mainly for required annual vacuum-sweeping activities, while for green roofs, it is used to carry out cleansing and vegetation maintenance. The area that installs this new catchment measure and the unit cost determines the total maintenance cost. The calculation of revenues is based on rainfalls, recycle efficiency and storage capacity, as indicated in Equation (9). ACk ¼

RNk X

   max 0; RQik  Areatotal  DCB  min SCp ; RQik  Areap

i¼1

     minðSCr ; RQik  Arear Þ  Uf þ Uc  min SCp ; RQik  Areap   Rep þ minðSCr ; RQik  Arear Þ  Rer þ Areac  UmA þ Areap  Ump þ Arear  Umr (5) DCB ¼ Areac  Dc

(6)

SCr ¼ Arear  ðDrc  Pr þ Drs Þ

(7)

SCp ¼ Areap  Dp  Pp

(8)

ARk ¼

RNk X 

  min SCp ; RQik  Areap  Rep þ minðSCr ; RQik  Arear Þ

i¼1

  Rer  Prk

Step 2: Uncertainty analysis

Uncertainty analysis addresses two research objectives: generate a wide range of scenarios of major uncertainty sources, and evaluate the performance of the design alternatives under the scenarios. To simplify the analysis, only two major uncertainty sources are identified at the current stage: price of water and rainfall. More uncertainty drivers can be introduced if needed.

4.3.1.

Scenarios generation

For the unit water price, the study relies on Geometric Brownian Motion (GBM) Process, captured by Equation (11) with drift assumed to be 1%, volatility 2% and Pr0 1.7$/m3. The assumptions come from the discussion with design team members. Based on these assumptions, 2000 scenarios consisting of annual unit water price for 50 years are generated (Fig. 1). dPt ¼ mPt dt þ sPt dWt m  drift; s  volatility; Wt  Wiener Process

(11)

As for the scenarios of rainfalls, the following assumptions are made: 1) Two major types of rain events are considered: normal rain events and storms. 2) Normal rain events are simulated using only one scenario. 3) Scenarios of storms are generated from IDF curves that are constructed by a company monitoring the rainfalls in Singapore. 4) Return period: 10 years. Based on Public Utilities Board (PUB) code of practice for surface water drainage (Code of Practice-Drainage Design and Considerations, 2011), since the area is less than 100 ha, a return period of 10 years is sufficient. The return period of each IDF curve also indicates the probability of the scenario. For example, for the scenario that has a return period of 1 month, the probability that it can happen in a specific day is 1/30. This assumption also indicates that only the ten IDF curves with return periods no more than 10 years are used to simulate storms. 5) Duration of a single rain event is normally distributed between 5 min and 420 min, with a mean of 60 and a variance of 100. 6) Only one rain event occurs in a single day.

(9) NPVB ¼ CAPEXB þ

50 X ARk  ACk k

k¼1

ð1 þ drÞ

(10)

Based on the aforementioned assumptions and models, the deterministic analysis is carried out, where the two design alternatives are evaluated under deterministic values of unit water price, the number of rain events and the rainfall in a single rain event (Prk ¼ 1.7$/m3, RNk ¼ 178, RQik ¼ 13.16 mm, ci,k). Table 2 summarizes the computation results. The deterministic DCF analysis shows that overall introducing porous pavements and green roofs may be more cost beneficial than the canal expansion alternative, as the former shows a less negative NPV compared with design A.

Under the assumptions above, the rainfall scenarios during the life cycle of the project have been simulated as follows (Fig. 2): 1) Reverse engineering of the IDF curves by using nonlinear regression to calibrate the relationship between rain durations and intensities. 2) Calculate the rainfall of the normal rain event using the equations in Fig. 2. 3) Apply the procedures described in the dashed box of Fig. 2 to generate the rainfall scenario of a single day. 4) Repeating step 3) by 365  50  2000 times, 2000 scenarios of daily rainfalls in 50 years are obtained. A histogram is built to show the distribution of daily rainfalls (Fig. 3) (Days without rain events are not counted).

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Fig. 3 e Histogram of 2000 scenarios of daily rainfalls in 50 years.

4.3.2.

Evaluation results

Subsequently to the scenario generation, the costs and benefits of the two design alternatives are evaluated under each simulated scenario. Equation (12) is used to calculate ENPV in this study. Here, NPVn is the net present value under the nth path of the uncertain factors, and pn is the probability of nth path. In this analysis, for simplicity of computation, every path is assumed to have the same probability, which here is 1/2000 since 2000 paths are generated. ENPV ¼

2000 X

pn  NPVn

(12)

n¼1

Combined with results from the deterministic analysis in the previous section and the uncertainty analysis, a probabilistic distribution (Fig. 4) and a multi-criteria comparison table (Table 3) are constructed.

As indicated from the above results, if only the deterministic analysis is referred as the basis of decision-making, although the ranking of design alternatives remains the same, the economic value of two design alternatives is either overestimated or underestimated. For design A, as shown in the cumulative probability curve, the likelihood that the realized NPV is smaller than the deterministic NPV is 1, which means the probability that such NPV can be obtained in the reality is negligible. This finding is supported by the Jensen’s (1906) inequality shown in Equation (13). As we take the average of uncertainty drivers (unit price, rainfall quantity and number of rainfall events), the NPV in the upside scenarios cannot be averaged out by the downside scenarios. In fact, since here the flood cost is incurred when the rainfall is higher than the drainage capacity, as long as the assumed deterministic value of single rainfall is lower than the drainage capacity, there is no flood damage cost resulted in

Fig. 4 e Distribution of NPV of design A and design B.

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Table 3 e Multi-metrics table of design A and design B. Deterministic NPV

ENPV

P5(VAR)

P95(VAG)

Standard deviation

$266,846 $252,274 Design B

$310,207 $90,956 Design B

$321,648 $103,443 Design B

$299,584 $78,419 Design B

$6,673 $7,557 Design A

Design A Design B Better Design

the whole life cycle of the system. In reality, however, the rainfall is subjected to high fluctuations, which leads to the presence of storms that lead to flood damage cost. The Flaw of Averages (Savage, 2000) is also observed in the result of design B but just turns out in an opposite direction. As shown in Fig. 4, the deterministic value of NPV is even away from the lower tail of the CDF curve, which means the chance of obtaining such a low NPV in real world is very slim. As for the standard deviation, since design A is only subjected to the fluctuation of rainfall, while design B is influenced by rainfall and price of water, the variance of design A is relatively lower. E½f ðxÞsf ðE½xÞ

4.3.3.

(13)

Further discussions

To further investigate how the two design alternatives perform under different scenarios, especially on the aspect of preventing flood damage, the flood damage costs under different rainfalls ranging from 0 mm to 300 mm are calculated. Fig. 5 shows the computation results. Based on Fig. 5, when the rainfall is higher than 20 mm, flood damage occurs to design B, while this threshold is almost doubled for design A. This indicates that there is a higher chance of flood damage in design B. Besides, since the rainfall in a single rain event is rarely higher than 160 mm (shown in Fig. 3), mostly higher flood damage costs happen to design B rather than design A. This seemly counter-intuitive result may come from the fact that only a small proportion of the test area (25%) can be deployed to either green roofs or porous pavements. Therefore the rain dropping to other area that is not covered by the new technology can only be evacuated through existing drainage canals. Meanwhile, compared with design A that expands the capacity of canals, the drainage capacity in design B is much smaller. Because of the reasoning above, design B is more vulnerable to rainfall fluctuations in terms of flood damage.

4.4.

Step 3: Flexibility analysis

To further improve the life cycle performance of the two design alternatives, this study proceeds with flexibility analysis. An expansion option is incorporated into both design A and design B, which is enabled by deploying a smaller capacity initially but reserving the necessary resources (e.g. land and capital) for possible future expansion. The process of generating flexible designs is a topic of active research (Cardin et al., 2013). Here, only one strategy is considered for demonstration purposes, although more real options opportunities exist (e.g. early abandonment, switching between different technologies, etc.)

4.4.1.

Flexible designs

For design A, the flexible design is as follows. The existing canals are not expanded at the beginning. If the number of

floods happening within one year exceeds ten times, the drainage capacity will be expanded until it reaches the upper bound (5000 m3). This expansion option is further explained using the following expressions: if

RNk X

1RQ ik Areatotal DCA ðRQ ik Þ  10 & ðDCA þ ExpSizeÞ  max A

i¼1

Then Capacity Expansion ¼¼ true 1RQ ik Areatotal DCA ðRQ ik Þ is the indicator function of RQ ik As for design B, the same area is deployed for the new technology but only half of the depth is deployed for the pavements and the underneath space of roofs. If the number of floods happening within one year exceeds ten times the storage capacity will be expanded by enlarging the depth until it reaches the upper bound. Details of this expansion option are shown below. For green roofs, if

RNk X

1RQ ik Arear SCr ðRQ ik Þ  10 & ðSCr þ ExpSizeÞ  maxr

i¼1

Then Capacity Expansion ¼¼ true 1RQ ik Arear SCr ðRQ ik Þ is the indicator function of RQ ik For porous pavements, if

RNk X

  1RQik Areap SCp ðRQik Þ  10 & SCp þ ExpSize  maxp

i¼1

Then Capacity Expansion ¼¼ true 1RQik Areap SCp ðRQik Þ is the indicator function of RQ ik

4.4.2.

Evaluation results

The two flexible designs are evaluated under the same 2000 scenarios generated in the uncertainty analysis. By summarizing results from the flexibility analysis and the uncertainty analysis, Fig. 6 and Table 4 are obtained. Fig. 6 shows the distribution of the NPV of all alternatives, while Table 4 summarizes the information on the predefined metrics. For design B, based on Equation (14), the value of flexibility is $105,799. The results show that incorporating flexibility makes design B profitable as ENPV turns out to be positive. One interesting observation is that the value of flexibility closely corresponds to the difference in CAPEX between flexible design B and baseline design B ($121,875). This indicates that baseline design B may be designed with unnecessary storage capacity whereas flexible design B gains the advantage by reducing the redundant initial investment. This is further confirmed by the fact that among the 2000 times of simulation, porous pavements are expanded only in a small proportion of scenarios (197 out of 2000), and it has never

w a t e r r e s e a r c h 4 7 ( 2 0 1 3 ) 7 1 6 2 e7 1 7 4

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Fig. 5 e Flood functions of design A and design B.

Fig. 6 e Distribution of NPV of all design alternatives.

reached the maximum capacity, while the expansion option is never exercised for green roofs. VoFB ¼ ENPVfb  ENPVb

(14)

For design A, the economic performance is also improved by considering the flexibility of a staged capacity deployment approach. According to Table 4, the extra value brought by this

Table 4 e Multi-metrics comparison table of all design alternatives. ENPV Design A Design B Flexible A Flexible B Better Design

$310,207 $90,956 $265,367 $14,843 Flexible B

P5(VAR) P95(VAG) $321,648 $103,443 $297,644 $3121 Flexible B

$299,584 $78,419 $234,641 $30,151 Flexible B

Standard deviation $6673 $7,557 $19,331 $11,486 Design A

expansion option is $44,840. The expansion decisions made through the simulation indicate that the improvement on design A is also achieved through reducing excessive capacity of the inflexible design. It is found that in less than 10% of the simulation does the drainage capacity of canals expands above 4000 m3, and mostly (over 70%) a capacity of 3520 m3 is considered sufficient based on the decision rule. The trade-off between the economy of scale and the time value of money may be another factor that leads to the better performance of flexible design A. The influence from the economy of scale suggests that a larger capacity deployed all at once is a more economic decision, while the time value of money favors that more investment should be placed later. In the case of design A, the latter factor seems to impose more impact on the final result.

4.5.

Step 4: Sensitivity analysis

After the flexibility analysis has been carried out, the best design alternative, flexible design B in this case study, is

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Fig. 7 e Sensitivity analysis of ENPVfb.

selected and subjected to the sensitivity analysis. Namely, the performance of flexible design B is reevaluated under the change of major assumptions made in Table 1. Recycle efficiency, maintenance cost, treatment cost, discounted rate expansion cost, and flood damage cost are assumed to be major influences on the performance of flexible design B. OFAT is applied in the sensitivity analysis. The values of the aforementioned factors are varied by 20% and 5% at a time, and then the ENPV of flexible design B is reevaluated under the new inputs. According to Fig. 7, the variation of expansion costs imposes almost no influence on the ENPV. This evidence

supports the conclusion made on the flexibility analysis, that the expansion is rarely exercised. On the other hand, the recycle efficiency of green roofs is shown to affect the performance of flexible design B most, which is even stronger than that of the discounted rate. The observation here contrasts to the recycle efficiency of porous pavements that does not influence the result so much. This difference between porous pavements and green roofs is also observed on the maintenance cost where green roofs lead to a stronger degree of changes on the ENPV. The observation may be resulted from the fact, that a larger area is deployed for roofs so that the ENPV depends more on the change of roofs. Water

Fig. 8 e Sensitivity analysis of VoFB.

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treatment cost also influences the result to a certain degree that is close to that of the maintenance cost of pavements, but higher than that of the unit flood cost. The relatively weak effect of unit flood cost may be explained by the low frequency of flood. This result also indicates the robustness of choosing design B, as in the worst case, the ENPV of flexible design B is still far better than flexible design A. Even a higher unit flood cost cannot diminish the advantage of flexible design B. By varying the same factors, this study also applies the OFAT to the VoFB. Results are shown in Fig. 8. Due to the negligible influence of expansion cost and maintenance cost on the result, Fig. 8 does not include these factors. According to Fig. 8, discounted rate is the most critical factor on the VoF. The result on discounted rate also corresponds to the conclusion made in the flexibility analysis that a higher discounted rate contributes to a higher VoF. It is also interesting to note that increasing recycle efficiency of pavements leads to lower value of flexibility. One reason for this observation is that higher recycle efficiency may prefer developing a larger capacity at the beginning so as to generate more revenues by re-using more rainwater. On the contrary, the influence from the recycle efficiency of roofs is almost negligible. This is explained by the fact that the capacity of roofs is never expanded in the simulation. Treatment cost and flood damage cost only have a slight effect on the result.

5.

Discussion and conclusions

The analysis presented in this paper demonstrated how to explicitly incorporate uncertainty and flexibility into the design and evaluation of urban water management systems. Through relevant literature, it has been shown that the typical system design approach and evaluation might lead to suboptimal system performance and flaws in the evaluation results (de Neufville & Scholtes, 2011). This finding was also confirmed by uncertainty analysis of the water catchment site in this study, which showed that the deterministic analysis resulted in considerably inaccurate evaluation of design alternatives. One advantage of applying the described methodology into systems design is the effectiveness in improving the life cycle performance. For example, for flexible design B in the application analysis, the extra benefits were brought by reducing the initial excessive capacity, and by enabling an expansion option, so that the system was able to avoid unnecessary initial investment if downside scenarios happened (e.g. low cost savings by “grey water” that could not balance the cost of the system). Meanwhile, the system was prepared to handle upside scenarios (e.g. high unit price of water which made the system more profitable). This action was similar to buying insurance for the system by which the distribution of the system performance was shifted to the right side. This improvement on economic performance resulted from incorporating flexibility was also observed on design A. However, flexible designs may not always result in improvement on system performance. As shown in the sensitivity analysis, there were many factors one would need to consider, such as the time value of money and opportunity cost. Although in the case study flexible design B was shown to be the best even under variations of assumptions, when

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faced with different systems, designers need to be careful about the trade-offs between those factors so that the system performance can be maximized. The framework and procedures introduced in this study can be generalized into the applications of other urban water management systems. The four-step analysis (baseline model building, uncertainty analysis, flexibility analysis and sensitivity analysis) is one example that can be applied to a wide range of water systems. Whereas since different systems are subjected to distinct costs and benefits, and faced with their respective source of uncertainties, details of modeling and computation may need to be adjusted to suit the particular system at hand. Another contribution of this analysis is combining historical data and IDF curves to simulate daily rainfall scenarios. The model can be easily modified to another region with different IDF curves or requirements of return periods. There are some limitations in this study. First, in the case study, the analysis has not accounted for all possible benefits. For example, for design B, the benefit of reduced mosquito breeding resulting from reduced standing water is not included. This case study should be considered as a first analysis of the major costs and benefits involved in this new water catchment technology. Follow-up contribution can be made to identify proper models to capture a more comprehensive picture of such systems. Second, only two flexible designs are considered in the application. It is highly possible that the economic performance of the system can be further enhanced by a better flexible design. Therefore, another opportunity of extending the study is to explore better methods to assist the conceptual design of flexible urban water management systems. The concept generation technique proposed by Cardin et al. (2013) is one option to assist such process. Finally, future research can also focus on introducing stochastic optimization analysis on the design of flexible urban water management systems, so that better design configurations will be identified. Optimization techniques, like the screening model proposed by Wang (2005) may be applied to accelerate the efficiency of doing optimization analysis.

Acknowledgments The authors are thankful for the financial support provided by the National University of Singapore (NUS) Faculty Research Committee via MOE AcRF Tier 1 grant WBS R-266000-061-133. The financial support provided by NUS Research Scholarship is also acknowledged. The authors would like to thank to the ISE department of NUS and Singapore-Delft Water Alliance for supporting this research work. Also, the authors would like to give thanks other colleagues in Dr. Cardin’s research group, who gave critical feedback on the completion of this work.

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