1
Valuing Flexibilities in the Design of Urban 1
Water Management Systems 2
Yinghan Deng1, Michel-Alexandre Cardin1*, Vladan Babovic2, 3, Deepak 3
Santhanakrishnan1, Petra Schmitter2, Ali Meshgi2 4
1Department of Industrial and Systems Engineering, National University of 5
Singapore 6
Block E1A #06-25, 1 Engineering Drive 2, 117576, Singapore 7
2Singapore-Delft Water Alliance 8
Block E1 #08-25, 1 Engineering Drive 2, 117576, Singapore 9
3Department of Civil & Environmental Engineering, National University of 10
Singapore 11
Block E1A, #07-03, 1 Engineering Drive 2, 117576, Singapore 12
Abstract 13
Climate change and rapid urbanization requires decision-makers to develop 14
a long-term forward assessment on sustainable urban water management 15
projects. This is further complicated by the difficulties of assessing 16
sustainable designs and various design scenarios from an economic 17
standpoint. A conventional valuation approach for urban water management 18
projects, like Discounted Cash Flow (DCF) analysis, fails to incorporate 19
uncertainties, such as amount of rainfall, unit cost of water, and other 20
uncertainties associated with future changes in technological domains. Such 21
approach also fails to include the value of flexibility, which enables 22
managers to adapt and reconfigure systems over time as uncertainty unfolds. 23
* Corresponding author. Tel: +65 6516 5387 Email: [email protected]
*ManuscriptClick here to download Manuscript: manuscript_revised2_clean_v2.doc Click here to view linked References
2
This work describes an integrated framework to value investments in urban 24
water management systems under uncertainty. It also extends the 25
conventional DCF analysis through explicit considerations of flexibility in 26
systems design and management. The approach incorporates flexibility as 27
intelligent decision-making mechanisms that enable systems to avoid future 28
downside risks and increase opportunities for upside gains over a range of 29
possible futures. 30
A water catchment area in Singapore was chosen to assess the value of a 31
flexible extension of standard drainage canals and a flexible deployment of 32
a novel water catchment technology based on green roofs and porous 33
pavements. Results show that integrating uncertainty and flexibility 34
explicitly into the decision-making process can reduce initial capital 35
expenditure, improve value for investment, and enable decision-makers to 36
learn more about system requirements during the lifetime of the project. 37
Keywords: Urban water management systems; Real options analysis; 38
Engineering system design and evaluation 39
1 Introduction 40
Traditional water resources planning and analysis methods are based on 41
requirements that are unrealistically deterministic (Medellín-Azuara et al., 42
2007). Under such considerations, the most common practice consists of 43
three phases. First, after relevant data is collected and analyzed, the most 44
likely scenarios are identified, which include projections of major 45
exogenous drivers of the system, such as markets, government policy, and 46
climate change. Then, according to those predictions, system designers 47
generate design concepts and select design parameters that enable the 48
system to perform optimally under the predictions. Economic evaluation of 49
the design is then conducted, of which standard methodology, like 50
3
discounted cash flow (DCF) analysis, optimization, and scenario planning, 51
is applied to achieve the best optimal design (de Neufville & Scholtes, 52
2011). 53
Such kind of design practice based on deterministic forecasts and the 54
assumption of fixed design parameters, however, may not provide a design 55
that performs best in the real world. First, the typical approach does not 56
capture the socio-technical and economic uncertainties that affect the water 57
resources systems, which ultimately shapes the efficacy of water supply 58
systems (S. X. Zhang & Babovic, 2011)– e.g. markets, regulations, and 59
technology. Such system as designed to be optimal in a specific realization 60
of the future achieves the expected performance only when the predicted 61
scenario is realized. Besides, standard design and evaluation analysis, which 62
uses expected values as inputs, may also mislead decision makers, and lead 63
to incorrect design decisions (de Neufville & Scholtes, 2011). This is 64
because the output response (e.g. economic value, rainfall drainage or 65
storage) of most complex systems today is not linear, and the performance 66
observed in downside scenarios cannot be balanced by the upside scenarios. 67
Such situation is described as “flaw of averages” (Savage, 2000). 68
Furthermore, the conventional approach of DCF is not able to capture 69
managerial flexibility (Trigeorgis, 1996). The sequence of decisions is 70
embedded over time in the cash flow profile as irreversible investment at t = 71
0. The system is assumed to remain “passive” and even though in reality 72
managers would try and adapt to the environment so as to capture better 73
economic performance. Standard DCF does not account for such flexibility 74
which may consequently leads to an underestimation of the performance of 75
systems and veils the ability of systems in managing uncertainties. Due to 76
the reasoning above, a paradigm shift in systems design and evaluation is in 77
need. 78
4
Flexibility in engineering design is one avenue to deal with uncertainty pro-79
actively. In this case, flexibility-also referred as real options-is defined as 80
the “right, but not the obligation, to change a project in the face of 81
uncertainty”(Trigeorgis, 1996). This different perspective on systems design 82
and evaluation is characterized by considering a wide range of possible 83
future scenarios and taking pro-active actions to mitigate critical uncertainty 84
sources. There are several applications of this methodology on large-scale 85
infrastructure systems (Babajide et al., 2009; Buurman et al., 2009; Cardin 86
et al., 2008; Michailidis et al., 2009), which have demonstrated that 87
incorporating flexibility considerably improves the life cycle performance 88
of systems. One typical example of flexible engineering designs in the real 89
estate sector is the Health Care Service Corporation (HCSC) building in 90
Chicago. In 1997, the building was initially designed to prepare for 91
expansion if demand for working space reached a certain level in the future. 92
The second phase of the vertical expansion option was exercised in 2010 93
(Guma et al., 2009). 94
The rest of this paper is organized as follows. The next section discusses the 95
motivations to apply the aforementioned approach, which considers 96
explicitly uncertainty and flexibility, to designing and evaluating urban 97
water management systems. The relevant literature is reviewed, and the 98
research gap for further contribution is identified. Following this section, the 99
details of the proposed methodology in this paper are introduced. Then a 100
case study on a novel water infrastructure system is presented, as to 101
demonstrate the implementation of the proposed methodology as well as its 102
effectiveness in terms of improving performance of the target system. 103
Finally discussions and conclusions are made in the last section. 104
5
2 Motivation 105
The world is experiencing a high rate of urbanization. For those countries 106
with highly urbanized population, like Singapore (100% of total population 107
in 2010), the size of urban population is still growing; while for countries 108
which are not highly urbanized at the current stage, like China (47% of total 109
population in 2010), the rate of urbanization change is high ("Urbanization," 110
2012). Increasing urbanization worldwide could intensify local competition 111
for all types of resources, water being amongst the most vital (Zoppou, 112
2001). In addition, many other factors, like land scarcity, climate change, 113
and depleting energy resources, require urban system designers to think 114
forward and provide efficient solutions that make better use of resources and 115
maintain sustainability. 116
Development of sustainable water systems has been subjected to heated 117
discussions recently. These systems are defined as “water systems that are 118
managed to satisfy changing demands placed on them (both human and 119
environmental) now and into the future, whilst maintaining ecological and 120
environmental integrity of water” (UNESCO, 1998). However, for such 121
emerging sustainable urban water management systems, we lack knowledge 122
of how sustainable development should be attained and how sustainability 123
of various technical systems should be assessed (Hellstrom et al., 2000). 124
Traditional water resources planning and analysis methods based on fixed 125
requirements and design parameters do not address how to properly evaluate 126
systems under uncertainties as well as how to effectively manage 127
uncertainties that are pervasive in urban systems of today. Some studies 128
have been proposed to support the decision process to manage urban water 129
(Makropoulos et al., 2008; Pearson et al., 2009; Thomas & Durham, 2003). 130
Results from these studies provide suggestions and tools on selection of 131
design alternatives and making policies. For example, Integrated Water 132
Resource Management (IWRM) is proposed to support the management of 133
6
alternative water resources from multiple perspectives (Thomas & Durham, 134
2003). Those studies, however, have not explicitly accounted for the various 135
sources of uncertainties, like instability of technical efficiency or fluctuation 136
in rainfall that may impact the results of decision-making. Some of the 137
recent studies have taken one step further to recognize the exogenous and 138
endogenous uncertainties faced by water systems, and even explicitly take 139
those uncertainties into account when doing evaluation analysis. For 140
example, Morimoto and Hope (2001, 2002) applied probabilistic techniques 141
to the cost-benefit analysis of hydroelectric projects in Sri Lanka, Malaysia, 142
Nepal, and Turkey, where they generated Net Present Value (NPV) 143
distribution for design alternatives. Their analysis, however, has not 144
incorporate pro-active actions to handle situations that may go beyond 145
designers’ predictions. Even though sensitivity analysis is conducted, it 146
merely acts as one part of the evaluation process and not as a way of 147
inspiring novel solutions to optimize the design itself. In some studies (Pahl-148
Wostl et al., 2007), Adaptive Management is introduced into urban water 149
management. These works, however, mainly deal with the operational part 150
of the systems and have not revealed how to make changes to design 151
configurations of the system as well as how to measure the additional 152
benefits brought by those changes. 153
In light of the situation explained above, this study considers applying 154
flexibility in engineering design thinking to planning and assessment of 155
urban water management systems. It has been indicated that incorporating 156
flexibility into systems can bring about performance improvements ranging 157
between 10% and 30%, compared to standard design and evaluation 158
approaches (de Neufville & Scholtes, 2011). These improvements are 159
achieved because flexible designs enable systems to hedge against downside 160
scenarios (e.g. by reducing the scale of initial capital expenditure) and 161
prepare for the unexpected favorable conditions (e.g. by allowing for future 162
expansion of the system). For example, in the case of Iridium and Globalstar, 163
7
the company would be able to reduce the life cycle cost by more than 20% if 164
a phasing deployment strategy could have been adopted (de Weck et al., 165
2004). 166
A set of procedures has been proposed in terms of designing and evaluating 167
flexibility in complex engineering systems (Cardin et al., 2008; Cardin et 168
al., 2007; S. X. Zhang & Babovic, 2011). One such procedure (Cardin et al., 169
2007) starts with conventional design and evaluation approaches, and then 170
further investigates into uncertainty and flexibility of the target system. 171
Although the detailed modeling of each system and its specific flexibility 172
varies from system to system, it is expected that those procedures and 173
frameworks can be modified and applied in the context of urban water 174
management systems. 175
Indeed, there were some recent studies already moving towards this 176
direction by using the real options approach to analyzing water systems. For 177
example, Zhang and Babovic (2012) have conducted real options analysis to 178
identify optimal water supply strategies, and Wang (2005) applied the 179
approach to optimize the development of a hypothetical river basin 180
involving decisions to build dams and hydropower stations. These studies 181
have indicated that by applying flexibility analysis to water systems, 182
designers are able to offer more cost-effective and sustainable solutions. 183
The main contribution of this paper is a systematic methodology to analyze 184
urban water management systems in an engineering context, considering 185
uncertainty and flexibility explicitly as part of the engineering design and 186
management process. The methodology is similar to the approaches used by 187
Zhang and Babovic (2012). However their work is mainly focused on 188
strategic policy making, while the methodology introduced in this paper is 189
rooted in an engineering design perspective. As for Wang’s study (Wang, 190
2005), the logic of doing the analysis is similar, but the target system of 191
Wang’s study is hydroelectric dams, which differ with urban water 192
8
management systems in terms of scale and complexity. Besides, the 193
uncertainties faced by these two kinds of water systems are also distinct. 194
Different modeling techniques need to be proposed so as to simulate the 195
behavior of the system and its uncertainty drivers in an urban context. 196
Furthermore, Wang applied mixed integer programming to modeling the 197
decision-making process and relied on dynamic programming in the aspect 198
of evaluation. This approach, however, imposes limitation on the decision 199
rules being evaluated, and may be trapped by curse of dimensionality when 200
confronted with a multitude of decision periods and states. The approach 201
here incorporates decision rules as another variable in the analytical model, 202
which enables modeling of diverse decision rules with relatively less 203
computational burden. Besides, it is a direct extension of existing design and 204
evaluation approaches, and is designed via a systematic step-wise process 205
for more practical impact in engineering practice. Another contribution from 206
a modeling standpoint involves the use of so-called Intensity Duration 207
Frequency (IDF) curves to simulate the rainfall behavior in order to 208
understand how rainfall intensities and durations as uncertainty factors may 209
influence the economic performance of the system. The last contribution is 210
to report on the first application of this methodology in the design and 211
deployment of porous pavement and green roof technologies, as a way to 212
recuperate and store grey water from natural rain events. Since not many 213
studies have been done, the study provides another example of how these 214
ideas can be considered in urban water management systems and how this 215
new catchment technology can be better deployed. It is hoped that the 216
results reported here will offer a different perspective on how to design, 217
evaluate and implement urban water management systems, which can be of 218
value to both research scholars and practitioners. 219
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3 Methodology 220
This study proposes a four-step procedure to design and evaluate flexible 221
urban water management systems. The procedure is based on and modified 222
from a design process proposed by a past study (Cardin et al., 2007). Similar 223
to the original one, this proposed methodology is also a step-wise process on 224
flexibility in design and evaluation, starting with the baseline model and 225
further stepping into the uncertainty analysis and the flexibility analysis. 226
One additional step of sensitivity analysis is added as to provide more 227
reliable analytical results. 228
3.1 Step 1: Baseline Model 229
The starting point of the methodology is to build a baseline model. The 230
objective here is to understand the main components of the system that 231
influence its full life cycle performance. Costs and benefits involved in the 232
system are calibrated by defining necessary design parameters and design 233
variables. Additionally, assumptions on the system are defined. Following 234
that, a preliminary deterministic cost-benefit analysis (Boardman et al., 235
2006) can be carried out. Generally, in this step, the conventional DCF 236
model is built to assess the performance of the system under the 237
deterministic conditions. This step captures the standard practice in terms of 238
design and project evaluation. 239
3.2 Step 2: Uncertainty Analysis 240
In this step, designers need to model major uncertainty drivers, and 241
investigate design alternatives under a range of possible future scenarios. 242
Historical data on the uncertainty drivers is collected and calibrated into 243
stochastic or probability models, like Geometric Brownian Motion (GBM) 244
and normal distribution. Then simulation is applied to generate scenarios 245
that are used to assess the life cycle performance of design alternatives. The 246
performance of these designs is compared under the criteria of Expected Net 247
Present Value (ENPV), VAG (Value At Gain, which quantifies the 248
10
performance in the upside scenarios), VAR (Value At Risk, which 249
quantifies the performance in the downside scenarios), and variance. 250
Through this analysis, designers capture a more comprehensive picture 251
about the pros and cons of the design alternatives, compared with the 252
deterministic analysis in Step 1. 253
3.3 Step 3: Flexibility Analysis 254
In this step, designers first need to generate flexible design concepts. A 255
complete flexible concept is defined by four elements: uncertainty source, 256
flexible strategy, flexible enabler, and decision rule (Cardin et al., 2012). 257
Flexible strategies are the actions designers can take when a particular path 258
of uncertainties is realized (e.g. expand the capacity of the system if demand 259
turns out to be higher than prediction), while flexible enablers are the design 260
configurations that make the strategies feasible from a design and 261
management standpoint. A decision rule is a triggering mechanism or an 262
“if” statement that specifies clearly when the flexible strategies will be 263
exercised, based on some uncertainty realizations. For example, in the case 264
of the HCSC building (Guma et al., 2009), the flexible concept can be “in 265
order to deal with the uncertainty from working space demand, extra 266
strength is added into the load bearing walls so that the building can be 267
expanded if the working space is not enough”. In this case, adding extra 268
strength is the flexible enabler and capacity expansion is the flexible 269
strategy, while the “if” statement about the working space is the decision 270
rule. 271
After flexible concepts are generated, they are evaluated under the same 272
scenarios and metrics stated in Step 2. The Value of Flexibility (VoF) is 273
calculated by equation (1). 274
275
(1) 276
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The computation of VoF can be resolved from several perspectives. The 277
classical works in pricing financial options (Black & Scholes, 1973; Cox et 278
al., 1979) are the origins of the valuation of real options. Later, the binomial 279
approach proposed by Cox et al. (1979) was suggested to value options on 280
real investments, hence real options (Trigeorgis, 1996). This approach has 281
also been applied to obtaining the value of real options in engineering 282
systems (de Weck et al., 2004). Decision tree is another method to assess 283
the VoF, when the number of decisions is limited and the uncertainty can be 284
modeled by discrete random variables. This method has been adopted to 285
evaluate the VoF in oil deployment projects (Babajide et al., 2009). An 286
important aspect of these two methodologies is that the evaluation process 287
relies on dynamic programming where the decision rule essentially is 288
decided by optimizing at each decision point based on expected value. This 289
kind of approach may not capture well the full realm of possible decision 290
rules. Besides, as the number of decision-making periods and states 291
increases, the computation may become intractable. Although the 292
assumption of path-independency in the binomial approach allows a 293
recombination structure to reduce computational burden, this assumption of 294
path-independency may not hold for engineering systems. This is because 295
different realizations of uncertainty may lead to different changes on system 296
configurations which in return result in different realizations in the next time 297
period (e.g. upgrading the efficiency of urban water systems may lead to 298
lower price of water next period). Another approach to obtain the VoF is 299
simulation. This approach can be more generally applied, since it has fewer 300
restrictions on the number of time periods being considered and the 301
distribution of uncertainties. Besides, this approach considers decision rules 302
as explicit variables in the modeling framework, so that the model itself can 303
be more easily modified to capture more diverse design configurations. 304
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3.4 Step 4: Sensitivity Analysis 305
Finally, sensitivity analysis is carried out in order to assess how the results 306
obtained following the above steps respond to changes in underlying 307
assumptions. This step can be seen as a way to test the robustness of the 308
design alternatives in response to the variation that may happen to the 309
assumptions. There are several standard mathematical methods that can be 310
applied in terms of doing sensitivity analysis. For example, one-factor-at-a-311
time method (OFAT) (Czitrom, 1999) is one of simplest and most common 312
approaches. 313
4 Application 314
In order to demonstrate an application of the methodology introduced 315
above, this study applies the approach to the feasibility analysis of a new 316
water technology. Besides, the results from this section also work as a 317
demonstration to show that the methodology is effective in terms of 318
improving the performance of urban water management systems. 319
4.1 Problem Definition 320
As part of an effort to investigate possible solutions for next-generation 321
water infrastructure systems, which aim to reduce damage caused by floods 322
in rainy seasons and re-use of the run-offs, a new technology based on 323
porous pavements and green roofs is being proposed. The technology allows 324
rainwater to infiltrate into the sub-surface layer where it is temporarily 325
stored. For porous pavements, the sub-surface layer is filled with porous 326
materials, while for the green roofs, the vegetation cover and space 327
underneath function as the storage facility. The stored rainwater is then 328
either detained in the ground, or be harvested by the pipe installed under 329
pavements or the underneath space of green roofs. Later this harvested 330
water can be recycled as “grey” water or be channeled to reservoirs. By 331
13
implementing this technology, revenues (as cost savings of re-using 332
rainwater) are generated. Besides, the porous pavements and green roofs 333
reduce frequency and peak flow rate of rainwater that enters the drainage 334
system. Consequently, less space is required for drainage, and the likelihood 335
of flooding damage is also reduced. (S. Zhang & Buurman, 2010) 336
A test site has been chosen for a preliminary analysis on the possibilities and 337
limitations of this innovative solution. The site is located within the Kent 338
Ridge campus of the National University of Singapore (NUS). The size of 339
the catchment has an area of about 8.2 ha. The land use distribution of the 340
catchment comprises the following: 41% of bushes, 35.5% of other green 341
areas, mostly grass patches on mild and steep slopes, 16.8% of rooftop and 342
4.77% of road areas. 343
There are two considered design alternatives: a traditional expansion of the 344
current drainage canal system (referred as design A) and alternative based 345
on catchment measures of porous pavements and green roofs (referred as 346
design B). Although design B has several aforementioned advantages 347
compared with design A, since design B incurs a higher construction cost 348
and maintenance cost, analysis is needed to better understand the costs and 349
benefits. Also, one aims to assess whether there is potential to further 350
improve the economic performance of those two design alternatives under 351
uncertainties by applying the flexibility analysis. 352
4.2 Step 1: Baseline DCF Model 353
The following is the list of notations used in the analysis. 354
Total area of the test site under study (m2) 355 Area that can be deployed to porous pavements (m2) 356 Area that can be deployed to green roofs (m2) 357
Drainage capacity of canals in design A (m3) 358 Drainage capacity of canals in design B (m3) 359
Depth of canals (m) 360 Area of existing canals (m2) 361 Area of expanded canals in design A (m2) 362
Storage capacity of porous pavements (m3) 363
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Storage capacity of green roofs (m3) 364 Depth of porous materials in porous pavements (m) 365 Depth of vegetation covers in green roofs (m) 366 Depth of underneath space in green roofs (m) 367
Porosity of porous materials in porous pavements 368 Porosity of vegetation covers in green roofs 369
Recycle efficiency of porous pavements 370 Recycle efficiency of green roofs 371
Initial investment of design A ($) 372 Initial investment of design B ($) 373
Unit flood damage cost ($/m3) 374 Unit maintenance cost of design A ($/m2) 375 Unit maintenance cost of porous pavements ($/m2) 376 Unit maintenance cost of green roofs ($/m2) 377
Unit cost of water treatment ($/m3) 378 Discounted rate 379
Annual cost in kth year ($) 380 Annual revenue in kth year ($) 381 Unit water price in kth year ($/m3) 382
Rainfall quantity of the ith rain of the kth year (m) 383 Number of rain events of the kth year 384
The assumptions for the design parameters and input data needed in the case 385
study are shown in Table 1. The cost information is based on personal 386
communications with the design team members (as shown in Table 1). 387
Although it may not be perfectly accurate, it is based on experienced 388
designers’ inputs and reflects the essence of the system to some degree. The 389
annual rainfall information is summarized from the online published data of 390
National Environmental Agency ("Weather Statistics," 2013). 391
Table 1 Assumptions on Parameters and Input Data 392
For design A, the following equations are developed. As there are no 393
mechanisms of generating revenues, the analysis only needs to quantify the 394
costs involved. There are two categories of costs under consideration. Flood 395
damage cost is calculated based on the occurrence of the rain events where 396
the rainfall quantity exceeds the drainage capacity. Maintenance cost is a 397
variable cost that links with the drainage area. The maintenance cost is 398
related to activities of physical cleansing, maintenance and minor structural 399
repairs of drains and canals. 400
401 (2) 402
15
403
(3) 404
405
(4) 406
As to design B, more refined equations are developed, since not only costs 407
need to be quantified but also the revenues generated as cost savings. In this 408
case, the extra rainwater, that can neither be evacuated through drainage 409
canals nor be captured by the new catchment measures, incurs flood damage 410
cost. For the existing drainage canals, the maintenance cost is estimated by 411
the same approach with design A. For porous pavements, the maintenance 412
cost is mainly for required annual vacuum-sweeping activities, while for 413
green roofs, it is used to carry out cleansing and vegetation maintenance. 414
The area that installs this new catchment measure and the unit cost 415
determines the total maintenance cost. The calculation of revenues is based 416
on rainfalls, recycle efficiency and storage capacity, as indicated in 417
Equation (9). 418
419
420 (5) 421
422
(6) 423
424
(7) 425
426
16
(8) 427
428
429
430 (9) 431
432
(10) 433
Based on the aforementioned assumptions and models, the deterministic 434
analysis is carried out, where the two design alternatives are evaluated under 435
deterministic values of unit water price, the number of rain events and the 436
rainfall in a single rain event ( =1.7$/m3, =178, =13.16mm, 437
). Table 2 summarizes the computation results. The deterministic DCF 438
analysis shows that overall introducing porous pavements and green roofs 439
may be more cost beneficial than the canal expansion alternative, as the 440
former shows a less negative NPV compared with design A. 441
Table 2 Results of Deterministic Analysis 442
4.3 Step 2: Uncertainty Analysis 443
Uncertainty analysis addresses two research objectives: generate a wide 444
range of scenarios of major uncertainty sources, and evaluate the 445
performance of the design alternatives under the scenarios. To simplify the 446
analysis, only two major uncertainty sources are identified at the current 447
stage: price of water and rainfall. More uncertainty drivers can be 448
introduced if needed. 449
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4.3.1 Scenarios Generation 450
For the unit water price, the study relies on Geometric Brownian Motion 451
(GBM) Process, captured by Equation (11) with drift assumed to be 1%, 452
volatility 2% and 1.7 $/m3. The assumptions come from the discussion 453
with design team members. Based on these assumptions, 2000 scenarios 454
consisting of annual unit water price for 50 years are generated (Figure 1). 455
* 456
* -drift, -volatility, -Wiener Process 457
(11) 458
Figure 1 2000 Scenarios of Annual Unit Water Price 459
As for the scenarios of rainfalls, the following assumptions are made. 460
1) Two major types of rain events are considered: normal rain events 461
and storms. 462
2) Normal rain events are simulated using only one scenario. 463
3) Scenarios of storms are generated from IDF curves that are 464
constructed by a company monitoring the rainfalls in Singapore. 465
4) Return period: 10 years. Based on Public Utilities Board (PUB) 466
code of practice for surface water drainage ("Code of Practice-467
Drainage Design and Considerations," 2011), since the area is less 468
than 100 ha, a return period of 10 years is sufficient. The return 469
period of each IDF curve also indicates the probability of the 470
scenario. For example, for the scenario that has a return period of 1 471
month, the probability that it can happen in a specific day is 1/30. 472
This assumption also indicates that only the ten IDF curves with 473
return periods no more than 10 years are used to simulate storms. 474
5) Duration of a single rain event is normally distributed between 5 475
minutes and 420 minutes, with a mean of 60 and a variance of 100. 476
6) Only one rain event occurs in a single day. 477
Under the assumptions above, the rainfall scenarios during the life cycle of 478
the project have been simulated as follows (Figure 2). 479
18
1) Reverse engineering of the IDF curves by using nonlinear 480
regression to calibrate the relationship between rain durations and 481
intensities. 482
2) Calculate the rainfall of the normal rain event using the equations 483
in Figure 2. 484
3) Apply the procedures described in the dashed box of Figure 2 to 485
generate the rainfall scenario of a single day. 486
4) Repeating step 3) by 365 x 50 x 2000 times, 2000 scenarios of 487
daily rainfalls in 50 years are obtained. A histogram is built to 488
show the distribution of daily rainfalls (Figure 3) (Days without 489
rain events are not counted). 490
Figure 2 Procedures of Generating Rainfall Scenarios 491
Figure 3 Histogram of 2000 scenarios of daily rainfalls in 50 492
years 493
4.3.2 Evaluation Results 494
Subsequently to the scenario generation, the costs and benefits of the two 495
design alternatives are evaluated under each simulated scenario. Equation 496
(12) is used to calculate ENPV in this study. Here, is the net present 497
value under the nth path of the uncertain factors, and is the probability of 498
nth path. In this analysis, for simplicity of computation, every path is 499
assumed to have the same probability, which here is 1/2000 since 2000 500
paths are generated. 501
502
(12) 503
Combined with results from the deterministic analysis in the previous 504
section and the uncertainty analysis, a probabilistic distribution (Figure 4) 505
and a multi-criteria comparison table (Table 3) are constructed. 506
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Figure 4 Distribution of NPV of Design A and Design B 507
Table 3 Multi-metrics Table of Design A and Design B 508
As indicated from the above results, if only the deterministic analysis is 509
referred as the basis of decision-making, although the ranking of design 510
alternatives remains the same, the economic value of two design alternatives 511
is either overestimated or underestimated. For design A, as shown in the 512
cumulative probability curve, the likelihood that the realized NPV is smaller 513
than the deterministic NPV is 1, which means the probability that such NPV 514
can be obtained in the reality is negligible. This finding is supported by the 515
Jensen’s inequality (Jensen, 1906) shown in Equation (13). As we take the 516
average of uncertainty drivers (unit price, rainfall quantity and number of 517
rainfall events), the NPV in the upside scenarios cannot be averaged out by 518
the downside scenarios. In fact, since here the flood cost is incurred when 519
the rainfall is higher than the drainage capacity, as long as the assumed 520
deterministic value of single rainfall is lower than the drainage capacity, 521
there is no flood damage cost resulted in the whole life cycle of the system. 522
In reality, however, the rainfall is subjected to high fluctuations, which leads 523
to the presence of storms that lead to flood damage cost. The Flaw of 524
Averages (Savage, 2000) is also observed in the result of design B but just 525
turns out in an opposite direction. As shown in Figure 4, the deterministic 526
value of NPV is even away from the lower tail of the CDF curve, which 527
means the chance of obtaining such a low NPV in real world is very slim. 528
As for the standard deviation, since design A is only subjected to the 529
fluctuation of rainfall, while design B is influenced by rainfall and price of 530
water, the variance of design A is relatively lower. 531
) 532
(13) 533
20
4.3.3 Further Discussions 534
To further investigate how the two design alternatives perform under 535
different scenarios, especially on the aspect of preventing flood damage, the 536
flood damage costs under different rainfalls ranging from 0mm to 300mm 537
are calculated. Figure 5 shows the computation results. 538
Figure 5 Flood Functions of Design A and Design B 539
Based on Figure 5, when the rainfall is higher than 20mm, flood damage 540
occurs to design B, while this threshold is almost doubled for design A. This 541
indicates that there is a higher chance of flood damage in design B. Besides, 542
since the rainfall in a single rain event is rarely higher than 160mm (shown 543
in Figure 3), mostly higher flood damage costs happen to design B rather 544
than design A. 545
This seemly counter-intuitive result may come from the fact that only a 546
small proportion of the test area (40.02%) can be deployed to either green 547
roofs or porous pavements. Therefore the rain dropping to other area that is 548
not covered by the new technology can only be evacuated through existing 549
drainage canals. Meanwhile, compared with design A that expands the 550
capacity of canals, the drainage capacity in design B is much smaller. 551
Because of the reasoning above, design B is more vulnerable to rainfall 552
fluctuations in terms of flood damage. 553
4.4 Step 3: Flexibility Analysis 554
To further improve the life cycle performance of the two design alternatives, 555
this study proceeds with flexibility analysis. An expansion option is 556
incorporated into both design A and design B, which is enabled by 557
deploying a smaller capacity initially but reserving the necessary resources 558
(e.g. land and capital) for possible future expansion. The process of 559
generating flexible designs is a topic of active research (Cardin et al., 2012). 560
Here, only one strategy is considered for demonstration purposes, although 561
21
more real options opportunities exist (e.g. early abandonment, switching 562
between different technologies, etc.) 563
4.4.1 Flexible Designs 564
For design A, the flexible design is as follows. The existing canals are not 565
expanded at the beginning. If the number of floods happening within one 566
year exceeds ten times, the drainage capacity will be expanded until it 567
reaches the upper bound (5000m3). This expansion option is further 568
explained using the following expressions. 569
570
571
572
* is the indicator function of 573 574
As for design B, the same area is deployed for the new technology but only 575
half of the depth is deployed for the pavements and the underneath space of 576
roofs. If the number of floods happening within one year exceeds ten times 577
the storage capacity will be expanded by enlarging the depth until it reaches 578
the upper bound. Details of this expansion option are shown below. 579
For green roofs, 580
581
582
* is the indicator function of 583 584
For porous pavements, 585
586
587
* is the indicator function of 588
589
22
590
4.4.2 Evaluation Results 591
The two flexible designs are evaluated under the same 2000 scenarios 592
generated in the uncertainty analysis. By summarizing results from the 593
flexibility analysis and the uncertainty analysis, Figure 6 and Table 4 are 594
obtained. Figure 6 shows the distribution of the NPV of all alternatives, 595
while Table 4 summarizes the information on the predefined metrics. 596
Figure 6 Distribution of NPV of All Design Alternatives 597
Table 4 Multi-metrics Comparison Table of All Design 598
Alternatives 599
For design B, based on equation (14), the value of flexibility is $105,799. 600
The results show that incorporating flexibility makes design B profitable as 601
ENPV turns out to be positive. One interesting observation is that the value 602
of flexibility closely corresponds to the difference in CAPEX between 603
flexible design B and baseline design B ($121,875). This indicates that 604
baseline design B may be designed with unnecessary storage capacity 605
whereas flexible design B gains the advantage by reducing the redundant 606
initial investment. This is further confirmed by the fact that among the 2000 607
times of simulation, porous pavements are expanded only in a small 608
proportion of scenarios (197 out of 2000), and it has never reached the 609
maximum capacity, while the expansion option is never exercised for green 610
roofs. 611
612
(14) 613
For design A, the economic performance is also improved by considering 614
the flexibility of a staged capacity deployment approach. According to 615
Table 4, the extra value brought by this expansion option is $44,840. The 616
expansion decisions made through the simulation indicate that the 617
23
improvement on design A is also achieved through reducing excessive 618
capacity of the inflexible design. It is found that in less than 10% of the 619
simulation does the drainage capacity of canals expands above 4000m3, and 620
mostly (over 70%) a capacity of 3520m3 is considered sufficient based on 621
the decision rule. The trade-off between the economy of scale and the time 622
value of money may be another factor that leads to the better performance of 623
flexible design A. The influence from the economy of scale suggests that a 624
larger capacity deployed all at once is a more economic decision, while the 625
time value of money favors that more investment should be placed later. In 626
the case of design A, the latter factor seems to impose more impact on the 627
final result. 628
4.5 Step 4: Sensitivity Analysis 629
After the flexibility analysis has been carried out, the best design alternative, 630
flexible design B in this case study, is selected and subjected to the 631
sensitivity analysis. Namely, the performance of flexible design B is 632
reevaluated under the change of major assumptions made in Table 1. 633
Recycle efficiency, maintenance cost, treatment cost, discounted rate 634
expansion cost, and flood damage cost are assumed to be major influences 635
on the performance of flexible design B. OFAT is applied in the sensitivity 636
analysis. The values of the aforementioned factors are varied by ± 20% and 637
5% at a time, and then the ENPV of flexible design B is reevaluated under 638
the new inputs. 639
According to Figure 7, the variation of expansion costs imposes almost no 640
influence on the ENPV. This evidence supports the conclusion made on the 641
flexibility analysis, that the expansion is rarely exercised. On the other hand, 642
the recycle efficiency of green roofs is shown to affect the performance of 643
flexible design B most, which is even stronger than that of the discounted 644
rate. The observation here contrasts to the recycle efficiency of porous 645
pavements that does not influence the result so much. This difference 646
24
between porous pavements and green roofs is also observed on the 647
maintenance cost where green roofs lead to a stronger degree of changes on 648
the ENPV. The observation may be resulted from the fact, that a larger area 649
is deployed for roofs so that the ENPV depends more on the change of 650
roofs. Water treatment cost also influences the result to a certain degree that 651
is close to that of the maintenance cost of pavements, but higher than that of 652
the unit flood cost. The relatively weak effect of unit flood cost may be 653
explained by the low frequency of flood. This result also indicates the 654
robustness of choosing design B, as in the worst case, the ENPV of flexible 655
design B is still far better than flexible design A. Even a higher unit flood 656
cost cannot diminish the advantage of flexible design B. 657
Figure 7 Sensitivity Analysis of ENPVfb 658
By varying the same factors, this study also applies the OFAT to the VoFB. 659
Results are shown in Figure 8. Due to the negligible influence of expansion 660
cost and maintenance cost on the result, Figure 8 does not include these 661
factors. According to Figure 8, discounted rate is the most critical factor on 662
the VoF. The result on discounted rate also corresponds to the conclusion 663
made in the flexibility analysis that a higher discounted rate contributes to a 664
higher VoF. It is also interesting to note that increasing recycle efficiency 665
of pavements leads to lower value of flexibility. One reason for this 666
observation is that higher recycle efficiency may prefer developing a larger 667
capacity at the beginning so as to generate more revenues by re-using more 668
rainwater. On the contrary, the influence from the recycle efficiency of roofs 669
is almost negligible. This is explained by the fact that the capacity of roofs 670
is never expanded in the simulation. Treatment cost and flood damage cost 671
only have a slight effect on the result. 672
Figure 8 Sensitivity Analysis of VoFB 673
25
5 Discussion and Conclusions 674
The analysis presented in this paper demonstrated how to explicitly 675
incorporate uncertainty and flexibility into the design and evaluation of 676
urban water management systems. Through relevant literature, it has been 677
shown that the typical system design approach and evaluation might lead to 678
suboptimal system performance and flaws in the evaluation results (de 679
Neufville & Scholtes, 2011). This finding was also confirmed by 680
uncertainty analysis of the water catchment site in this study, which showed 681
that the deterministic analysis resulted in considerably inaccurate evaluation 682
of design alternatives. 683
One advantage of applying the described methodology into systems design 684
is the effectiveness in improving the life cycle performance. For example, 685
for flexible design B in the application analysis, the extra benefits were 686
brought by reducing the initial excessive capacity, and by enabling an 687
expansion option, so that the system was able to avoid unnecessary initial 688
investment if downside scenarios happened (e.g. low cost savings by “grey 689
water” that could not balance the cost of the system). Meanwhile, the 690
system was prepared to handle upside scenarios (e.g. high unit price of 691
water which made the system more profitable). This action was similar to 692
buying insurance for the system by which the distribution of the system 693
performance was shifted to the right side. This improvement on economic 694
performance resulted from incorporating flexibility was also observed on 695
design A. 696
However, flexible designs may not always result in improvement on system 697
performance. As shown in the sensitivity analysis, there were many factors 698
one would need to consider, such as the time value of money and 699
opportunity cost. Although in the case study flexible design B was shown to 700
be the best even under variations of assumptions, when faced with different 701
26
systems, designers need to be careful about the trade-offs between those 702
factors so that the system performance can be maximized. 703
The framework and procedures introduced in this study can be generalized 704
into the applications of other urban water management systems. The four-705
step analysis (baseline model building, uncertainty analysis, flexibility 706
analysis and sensitivity analysis) is one example that can be applied to a 707
wide range of water systems. Whereas since different systems are subjected 708
to distinct costs and benefits, and faced with their respective source of 709
uncertainties, details of modeling and computation may need to be adjusted 710
to suit the particular system at hand. Another contribution of this analysis is 711
combining historical data and IDF curves to simulate daily rainfall 712
scenarios. The model can be easily modified to another region with different 713
IDF curves or requirements of return periods. 714
There are some limitations in this study. First, in the case study, the analysis 715
has not accounted for all possible benefits. For example, for design B, the 716
benefit of reduced mosquito breeding resulting from reduced standing water 717
is not included. This case study should be considered as a first analysis of 718
the major costs and benefits involved in this new water catchment 719
technology. Follow-up contribution can be made to identify proper models 720
to capture a more comprehensive picture of such systems. Second, only two 721
flexible designs are considered in the application. It is highly possible that 722
the economic performance of the system can be further enhanced by a better 723
flexible design. Therefore, another opportunity of extending the study is to 724
explore better methods to assist the conceptual design of flexible urban 725
water management systems. The concept generation technique proposed by 726
Cardin et al. (2012) is one option to assist such process. Finally, future 727
research can also focus on introducing stochastic optimization analysis on 728
the design of flexible urban water management systems, so that better 729
design configurations will be identified. Optimization techniques, like the 730
27
screening model proposed by Wang (2005) may be applied to accelerate the 731
efficiency of doing optimization analysis. 732
Acknowledgements 733
The authors are thankful for the financial support provided by the National 734
University of Singapore (NUS) Faculty Research Committee via MOE 735
AcRF Tier 1 grant WBS R-266-000-061-133. The financial support 736
provided by NUS Research Scholarship is also acknowledged. The authors 737
would like to thank to the ISE department of NUS and Singapore-Delft 738
Water Alliance for supporting this research work. Also, the authors would 739
like to give thanks other colleagues in Dr. Cardin’s research group, who 740
gave critical feedback on the completion of this work. 741
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Assumptions and Input Data Catchment area (m2) 82000 Pave area (m2) 7500 Roofs area (m2) 13000
Recycle efficiency (roofs) 0.45 Recycle efficiency (pavements) 0.65 Depth of canals (m) 0.5
Existing area of canals (m2) 2600 Expanded area of canals (m2) 5400 Porosity (pavements) 0.3
Depth (pavements) (m) 0.3 Porosity (roofs) 0.6 Depth (vegetation of roofs) (m) 0.15
Depth (space underneath of roofs) (m) 0.3 CAPEX (design A) ($) 150,000 CAPEX (design B) ($) 421,875
Maintenance cost (pavements) ($/m2) 1.0 Maintenance cost (roofs) ($/m2) 1.2 Maintenance cost (canals) ($/m2) 0.85
Water price ($/m3) 1.7 Water treatment cost ($/m3) 0.3 Flood damage cost ($/m3) 0.5
Average NO. of rain events (year) 178 Average rainfall in one rain (mm) 13.16 CAPEX (Flexible B) ($) 300,000
Expansion cost (pavements) ($/112.5m3) 70,000 Expansion cost (roofs) ($/650m3) 50,000 Expansion cost (canals) ($/740m3) 48,000
Table 1 Assumptions on Parameters and Input DataClick here to download Table: TAB1.docx
Design A Design B Best Design NPV ($) -266,846 -252,274 Design B
Table 2 Results of Deterministic AnalysisClick here to download Table: TAB2.docx
Deterministic NPV ENPV P5(VAR) P95(VAG) Standard deviation
Design A -$266,846 -$310,207 -$321,648 -$299,584 $6,673 Design B -$252,274 -$90,956 -$103,443 -$78,419 $7,557 Better Design Design B Design B Design B Design B Design A
Table 3 Multi-metrics Table of Design A and Design BClick here to download Table: TAB3.docx
ENPV P5(VAR) P95(VAG) Standard deviation
Design A -$310,207 -$321,648 -$299,584 $6,673 Design B -$90,956 -$103,443 -$78,419 $7,557 Flexible A -$265,367 -$297,644 -$234,641 $19,331 Flexible B $14,843 -$3,121 $30,151 $11,486 Better Design Flexible B Flexible B Flexible B Design A
Table 4 Multi-metrics Comparison Table of All Design AlternativeClick here to download Table: TAB4.docx
Figure 3 Histogram of 2000 scenarios of daily rainfalls in 50 yeClick here to download high resolution image
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