# Development of a Multiscenario Planning Approach for Urban Drainage Systems

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Model Overview

#### 2.2. Scenario Development

#### 2.3. Two-Phase Multi-Scenario-Based UDS Planning

#### 2.3.1. Phase I: Scenario-Optimal Planning Solution

^{i}is ith future scenario, which is a combination of different rainfall patterns and nodal inflow distributions; and G is a set of constraints that can be checked based on the UDS simulation under ω

^{i}. The PipeCC is expressed as

_{c}is the construction cost according to the unit cost of a pipe of a certain diameter per unit length (USD/m), L

_{j}is the length of the jth pipe (m), D

_{j}is jth pipe’s diameter (m), and N is the total number of pipes. The ManholeDC is computed according to

_{c}is the unit cost of a manhole (USD/m), MD

_{k}is the depth of kth manhole (m), and M is the total number of nodes.

_{k}is the flooding volume at node k (m

^{3}/s).

_{down}) is greater than or equal to that of the upstream pipe (D

_{up}), because it is more likely in practice that a greater volume of water is eventually drained downstream. The constraint for pipe diameters is expressed as follows:

_{min}):

#### 2.3.2. Phase II: Multi-Scenario-Based Planning Based on Component-Wise RC

^{1}*, X

^{2}*, …, X

^{i}*], obtained from Phase I, were analyzed to identify the common elements. For example, the potential diameter of a pipe that has a range of 0.76–1.22 m in the scenario-optimal solutions was limited in the identified range in seeking the compromise solution (Step 2). As with Phase I, Phase II was also solved using the SWMM linked with the HSA to seek a compromise solution.

_{i}is the RC in scenario i, which represents the sum of overpayments and supplementary payments in the system; and RC

_{max}is the allowable maximum RC. The total RC in scenario i is expressed as

^{i}* is scenario-optimal solution in scenario i, obtained from Phase I and X

^{comp}is the potential compromise solution generated by Phase II.

^{i}* and X

^{comp}.

#### 2.4. Study Network

## 3. Application Results

#### 3.1. Scenario-Optimal Planning Solution for Individual Scenarios (Phase I)

#### 3.2. Identification of Common Elements

#### 3.3. RC Computation

#### 3.4. Multi-Scenario-Based Planning Solution Based on Component-Wise Regret Cost (Phase II)

## 4. Summary and Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Deal, B. Ecological urban dynamics: The convergence of spatial modelling and sustainability. Build. Res. Inf.
**2001**, 29, 381–393. [Google Scholar] [CrossRef] - Deal, B.; Schunk, D. Spatial dynamic modeling and urban land use transformation: A simulation approach to assessing the costs of urban sprawl. Ecol. Econ.
**2004**, 51, 79–95. [Google Scholar] [CrossRef] - Deal, B.; Pallathucheril, V. Developing and Using Scenarios, in Engaging the Future: Forecasts, Scenarios, Plans, and Projects; Hopkins, L.D., Zapata, M.A., Eds.; Lincoln Institute for Land Policy: Cambridge, MA, USA, 2007; pp. 221–242. [Google Scholar]
- Choi, W.; Deal, B.M. Assessing hydrological impact of potential land use change through hydrological and land use change modeling for the Kishwaukee River basin (USA). J. Environ. Manag.
**2008**, 88, 1119–1130. [Google Scholar] [CrossRef] [PubMed] - Deal, B.; Pallathucheril, V. Sustainability and urban dynamics: Assessing future impacts on ecosystem services. Sustainability
**2009**, 1, 346–362. [Google Scholar] [CrossRef][Green Version] - Nanía, L.S.; León, A.S.; García, M.H. Hydrologic-hydraulic model for simulating dual drainage and flooding in urban areas: Application to a catchment in the metropolitan area of Chicago. J. Hydrol. Eng.
**2015**, 20, 04014071. [Google Scholar] - Akhter, M.S.; Hewa, G.A. The use of PCSWMM for assessing the impacts of land use changes on hydrological responses and performance of WSUD in managing the impacts at Myponga catchment, South Australia. Water
**2016**, 8, 511. [Google Scholar] [CrossRef] - Deal, B.; Pan, H.; Timm, S.; Pallathucheril, V. The role of multidirectional temporal analysis in scenario planning exercises and planning support systems. Comp. Environ. Urban Sys.
**2017**, 64, 91–102. [Google Scholar] [CrossRef] - Deal, B.; Pan, H. Discerning and addressing environmental failures in policy scenarios using planning support system (PSS) technologies. Sustainability
**2017**, 9, 13. [Google Scholar] [CrossRef][Green Version] - Liwanag, F.; Mostrales, D.S.; Ignacio, M.T.T.; Orejudos, J.N. Flood modeling using GIS and PCSWMM. Eng. J.
**2018**, 22, 279–289. [Google Scholar] [CrossRef] - Kapelan, Z.S.; Savic, D.A.; Walters, G.A. Multiobjective design of water distribution systems under uncertainty. Water Resour. Res.
**2005**, 41, 1–15. [Google Scholar] [CrossRef] - Cunha, M.D.C.; Sousa, J.J.D.O. Robust design of water distribution networks for a proactive risk management. J. Water Resour. Plan. Manag.
**2010**, 136, 227–236. [Google Scholar] [CrossRef] - Liu, Y.; Guo, H.; Zhang, Z.; Wang, L.; Dai, Y.; Fan, Y. An optimization method based on scenario analysis for watershed management under uncertainty. Environ. Manag.
**2007**, 39, 678–690. [Google Scholar] [CrossRef] [PubMed] - Makropoulos, C.K.; Natsis, K.; Liu, S.; Mittas, K.; Butler, D. Decision support for sustainable option selection in integrated urban water management. Environ. Model. Soft.
**2008**, 23, 1448–1460. [Google Scholar] [CrossRef] - Pallottino, S.; Sechi, G.M.; Zuddas, P. A DSS for water resources management under uncertainty by scenario analysis. Environ. Model. Soft.
**2005**, 20, 1031–1042. [Google Scholar] [CrossRef] - Maharjan, M.; Pathirana, A.; Gersonius, B.; Vairavamoorthy, K. Staged cost optimization of urban storm drainage systems based on hydraulic performance in a changing environment. Hydrol. Earth Syst. Sci.
**2009**, 13, 481–489. [Google Scholar] [CrossRef][Green Version] - Yazdi, J.; Lee, E.H.; Kim, J.H. Stochastic multiobjective optimization model for urban drainage network rehabilitation. J. Water Resour. Plan. Manag.
**2014**, 141, 04014091. [Google Scholar] [CrossRef] - Kang, N.; Kim, S.; Kim, Y.; Noh, H.; Hong, S.; Kim, H. Urban drainage system improvement for climate change adaptation. Water
**2016**, 8, 268. [Google Scholar] [CrossRef][Green Version] - Wang, M.; Sweetapple, C.; Fu, G.; Farmani, R.; Butler, D. A framework to support decision making in the selection of sustainable drainage system design alternatives. J. Environ. Manag.
**2017**, 201, 145–152. [Google Scholar] [CrossRef] - Kang, D.; Lansey, K. Scenario-based robust optimization of regional water and wastewater infrastructure. J. Water Resour. Plan. Manag.
**2013**, 139, 325–338. [Google Scholar] [CrossRef] - Kang, D.; Lansey, K. Multiperiod planning of water supply infrastructure based on scenario analysis. J. Water Resour. Plan. Manag.
**2014**, 140, 40–54. [Google Scholar] [CrossRef] - Ngo, T.T.; Jung, D.; Kim, J.H. Robust urban drainage system: Development of a novel multiscenario-based Design Approach. J. Water Resour. Plan. Manag.
**2019**, 145, 04019027. [Google Scholar] [CrossRef] - Schwartz, P. The Art of the Long View: Planning for the Future in An Uncertain World; Crown Business: New York, NY, USA, 1991. [Google Scholar]
- Huff, F.A. Time distribution of rainfall in heavy storms. Water Resour. Res.
**1967**, 3, 1007–1019. [Google Scholar] [CrossRef] - Rossman, L.A. Storm-Water Management Model User’s Manual Version 5.1; USEPA: Washington, DC, USA, 2015.
- Geem, Z.W.; Kim, J.H.; Loganathan, G.V. A new heuristic optimization algorithm: Harmony search. Simulation
**2001**, 76, 60–68. [Google Scholar] [CrossRef]

**Figure 1.**Schematic of regret cost (RC) concept at two levels. (

**A**) Overall system; (

**B**) individual components.

**Figure 5.**S-city urban drainage network. (a) northwestern corner; (b) midtown; and (c) southeastern corner sectors.

**Figure 6.**Flooding hydrograph in scenario-optimal solutions under corresponding individual scenarios. (

**a**) Second quartile and (

**b**) third quartile.

**Figure 7.**Optimal component dimensions obtained from the scenario-optimal solutions. (

**a**) pipe size and (

**b**) manhole depth.

**Figure 9.**Comparison of the final total costs between scenario-optimal solutions and multi-scenario-based compromise solution.

**Figure 10.**Comparison of the system performance between scenario-optimal solutions and multi-scenario-based compromise solution.

Planning/Scenario ^{a} | D1/S1 | D2/S2 | D3/S3 | D4/S4 | D5/S5 | D6/S6 | |
---|---|---|---|---|---|---|---|

Pipe | Cost ($M) | 1.466 | 1.462 | 1.318 | 1.372 | 1.823 | 1.357 |

Max. size (m) | 2.13 | 1.83 | 1.83 | 1.83 | 2.13 | 1.83 | |

Min. size (m) | 0.3 | 0.3 | 0.3 | 0.3 | 0.3 | 0.3 | |

Manhole | Cost ($M) | 0.205 | 0.190 | 0.203 | 0.195 | 0.194 | 0.162 |

Max. depth (m) | 4.0 | 4.0 | 4.0 | 3.6 | 3.6 | 3.6 | |

Min. depth (m) | 1.5 | 1.5 | 1.5 | 1.8 | 1.8 | 1.5 | |

Penalty | Cost ($M) | 0.601 | 0.507 | 0.372 | 0.609 | 0.127 | 0.382 |

System material cost ($M) | 1.671 | 1.652 | 1.521 | 1.567 | 2.017 | 1.519 | |

Total cost ($M) | 2.272 | 2.159 | 1.893 | 2.176 | 2.144 | 1.901 |

^{a}Scenario-optimal planning (P1 to P6) was the optimal solution corresponding to each scenario (S1 to S6).

Cost Categories | S1 | S2 | S3 | S4 | S5 | S6 | |
---|---|---|---|---|---|---|---|

Pipe construction cost | Optimal | 1.466 | 1.466 | 1.466 | 1.466 | 1.466 | 1.466 |

Overpayment | 0.000 | 0.242 | 0.418 | 0.278 | 0.173 | 0.404 | |

Supplementary payment | 0.000 | 0.238 | 0.270 | 0.184 | 0.530 | 0.296 | |

Total cost (optimal + RC) | 1.466 | 1.946 | 2.154 | 1.928 | 2.169 | 2.166 | |

Manhole depth cost | Optimal | 0.205 | 0.205 | 0.205 | 0.205 | 0.205 | 0.205 |

Overpayment | 0.000 | 0.034 | 0.029 | 0.024 | 0.025 | 0.050 | |

Supplementary payment | 0.000 | 0.019 | 0.027 | 0.014 | 0.014 | 0.007 | |

Total cost (optimal + RC) | 0.205 | 0.258 | 0.261 | 0.243 | 0.244 | 0.262 | |

System material costs | Optimal | 1.671 | 1.671 | 1.671 | 1.671 | 1.671 | 1.671 |

Overpayment | 0.000 | 0.276 | 0.447 | 0.302 | 0.198 | 0.454 | |

Supplementary payment | 0.000 | 0.257 | 0.297 | 0.198 | 0.544 | 0.303 | |

Total cost (optimal + RC) | 1.671 | 2.204 | 2.415 | 2.171 | 2.413 | 2.428 | |

Total RC | 0.000 | 0.533 | 0.744 | 0.500 | 0.742 | 0.757 | |

Penalty cost | 0.602 | 0.624 | 0.655 | 0.632 | 0.612 | 0.655 | |

Final total cost | 2.272 | 2.828 | 3.070 | 2.803 | 3.025 | 3.083 |

Scenarios | Cost Statistics | |||||||||
---|---|---|---|---|---|---|---|---|---|---|

Designs | S1 | S2 | S3 | S4 | S5 | S6 | E. C ^{a} | Stdv. ^{b} | E. RC ^{c} | E. RC/E. C |

D1 | 2.272 | 2.828 | 3.070 | 2.803 | 3.025 | 3.083 | 2.847 | 0.280 | 0.655 | 0.230 |

D2 | 2.726 | 2.159 | 2.658 | 2.584 | 2.824 | 2.487 | 2.573 | 0.213 | 0.494 | 0.192 |

D3 | 2.418 | 2.345 | 1.893 | 2.220 | 2.462 | 2.361 | 2.283 | 0.190 | 0.558 | 0.244 |

D4 | 2.570 | 2.548 | 2.678 | 2.176 | 2.873 | 2.689 | 2.589 | 0.212 | 0.526 | 0.203 |

D5 | 2.953 | 2.870 | 2.782 | 2.873 | 2.144 | 2.831 | 2.742 | 0.272 | 0.662 | 0.241 |

D6 | 2.711 | 2.216 | 2.340 | 2.384 | 2.601 | 1.901 | 2.359 | 0.263 | 0.542 | 0.230 |

^{a}E. C, expected cost;

^{b}Stdv., cost standard deviation;

^{c}E. RC, expected RC. Note, costs in bold denote the scenario-optimal cost under the corresponding scenarios.

Cost Categories | S1 | S2 | S3 | S4 | S5 | S6 | |
---|---|---|---|---|---|---|---|

Pipe construction cost | Overpayment | 0.346 | 0.274 | 0.440 | 0.365 | 0.144 | 0.368 |

Supplementary payment | 0.087 | 0.011 | 0.032 | 0.010 | 0.242 | 0.000 | |

Regret costs | 0.433 | 0.285 | 0.472 | 0.375 | 0.386 | 0.368 | |

Manhole depth cost | Overpayment | 0.009 | 0.018 | 0.010 | 0.006 | 0.012 | 0.034 |

Supplementary payment | 0.021 | 0.015 | 0.020 | 0.008 | 0.013 | 0.003 | |

Regret costs | 0.030 | 0.033 | 0.030 | 0.014 | 0.025 | 0.037 | |

Total regret cost | Overpayment | 0.355 | 0.292 | 0.450 | 0.370 | 0.156 | 0.402 |

Supplementary payment | 0.108 | 0.026 | 0.052 | 0.019 | 0.255 | 0.003 | |

Regret costs | 0.463 | 0.318 | 0.502 | 0.389 | 0.411 | 0.405 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Kwon, S.H.; Jung, D.; Kim, J.H. Development of a Multiscenario Planning Approach for Urban Drainage Systems. *Appl. Sci.* **2020**, *10*, 1834.
https://doi.org/10.3390/app10051834

**AMA Style**

Kwon SH, Jung D, Kim JH. Development of a Multiscenario Planning Approach for Urban Drainage Systems. *Applied Sciences*. 2020; 10(5):1834.
https://doi.org/10.3390/app10051834

**Chicago/Turabian Style**

Kwon, Soon Ho, Donghwi Jung, and Joong Hoon Kim. 2020. "Development of a Multiscenario Planning Approach for Urban Drainage Systems" *Applied Sciences* 10, no. 5: 1834.
https://doi.org/10.3390/app10051834