# Capacity Optimization of Rainwater Harvesting Systems Based on a Cost–Benefit Analysis: A Financial Support Program Review and Parametric Sensitivity Analysis

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## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. Financial Support Policies for Rainwater Harvesting Systems in South Korea

#### 2.2. Study Area

#### 2.3. Economic Analysis of Rainwater Harvesting Systems

#### 2.3.1. Cost–Benefit Analysis

#### 2.3.2. Discount Rate and Inflation Rate

#### 2.4. Optimum Capacity of Rainwater Harvesting Systems Considering Benefit–Cost Analysis

#### 2.4.1. Simulation Model for Rainwater Harvesting Systems

#### 2.4.2. Optimization Model to Determine the Capacity of Rainwater Harvesting Systems Considering Benefit–Cost Analysis

## 3. Results

#### 3.1. Water Balance Analysis of the Rainwater Harvesting System

#### 3.2. Comparative Evaluation of Two Cost–Benefit Analysis Methods

#### 3.3. Analysis of the Effectiveness of Financial Support Programs

#### 3.4. Sensitivity Analysis of the Discount Rate and Inflation Rate

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

BCR | Benefit–cost ratio |

NPV | Net present value |

RWH | Rainwater harvesting |

APSWR | Act for the Promotion and Support of Water Reuse |

PSO | Particle swarm optimization |

## Appendix A

Institution/Country | Social Discount Rate | Remark |
---|---|---|

World Bank | Projects for developing countries: 10–12% | |

United States Environmental Protection Agency | Intergenerational discount rate: 2–3% (subject to sensitivity analysis) | [56] |

European Union | Long-term projects/policies: 3% | [57] |

United Kingdom | Standard: 3.5% Long-term projects of 30–125 years: 3%; 125–200 years: 2%; 200+ years: 1.5% | [58] |

France | Standard: 4% Long-term projects/policies: 2% | [59] |

Netherlands | Standard: 5.5% Projects/policies for climate change: 4% | [60] |

Germany | Long-term projects/policies: 1% | |

Japan | Projects within 50 years: 4% | |

Australia | Standard: 7% Subject to sensitivity analysis: 3% and 10% | [20] |

China | Short- and mid-term projects: 8% Long-term projects: less than 8% | [61] |

India | 12% | |

Republic of the Philippines | 15% | |

South Korea | Standard: 4.5% Water resources projects of 0–30 years: 4.5%; 30+ years: 3.5% | [62] |

**Table A2.**The results of our sensitivity analysis of inflation and discount rates: the maximum net present value.

Classification | Inflation Rate | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

−1.1% | −0.2% | 0.8% | 1.7% | 2.6% | 3.5% | 4.5% | 5.4% | 6.3% | 7.2% | ||

Discount Rate | 1.5% | 447 | 550 | 677 | 837 | 1051 | 1318 | 1648 | 2053 | 2545 | 3144 |

1.9% | 412 | 508 | 623 | 769 | 958 | 1204 | 1504 | 1877 | 2328 | 2878 | |

2.2% | 380 | 468 | 575 | 707 | 876 | 1099 | 1374 | 1715 | 2131 | 2636 | |

2.6% | 352 | 432 | 531 | 651 | 803 | 1002 | 1256 | 1566 | 1950 | 2414 | |

3.0% | 326 | 398 | 490 | 601 | 739 | 915 | 1148 | 1432 | 1784 | 2211 | |

3.3% | 302 | 369 | 453 | 555 | 680 | 839 | 1048 | 1310 | 1631 | 2025 | |

3.7% | 280 | 342 | 418 | 513 | 627 | 771 | 957 | 1198 | 1491 | 1854 | |

4.1% | 260 | 317 | 386 | 474 | 580 | 711 | 877 | 1096 | 1365 | 1697 | |

4.4% | 242 | 294 | 358 | 438 | 536 | 655 | 805 | 1001 | 1250 | 1552 | |

4.8% | 225 | 272 | 332 | 404 | 496 | 605 | 742 | 915 | 1144 | 1421 |

Classification | Inflation Rate | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

−1.1% | −0.2% | 0.8% | 1.7% | 2.6% | 3.5% | 4.5% | 5.4% | 6.3% | 7.2% | ||

Discount Rate | 1.5% | 800 | 837 | 1015 | 1272 | 1602 | 1681 | 1895 | 1992 | 2093 | 2235 |

1.9% | 771 | 840 | 913 | 1054 | 1474 | 1611 | 1801 | 1942 | 2054 | 2222 | |

2.2% | 669 | 825 | 841 | 1032 | 1280 | 1597 | 1682 | 1917 | 1997 | 2096 | |

2.6% | 641 | 804 | 836 | 957 | 1122 | 1578 | 1638 | 1871 | 1951 | 2090 | |

3.0% | 633 | 720 | 823 | 843 | 1051 | 1344 | 1632 | 1732 | 1935 | 1997 | |

3.3% | 617 | 674 | 823 | 844 | 1014 | 1267 | 1607 | 1669 | 1897 | 1986 | |

3.7% | 624 | 635 | 773 | 826 | 894 | 1057 | 1470 | 1633 | 1786 | 1929 | |

4.1% | 537 | 628 | 668 | 823 | 840 | 1045 | 1280 | 1605 | 1692 | 1916 | |

4.4% | 502 | 622 | 680 | 820 | 858 | 987 | 1102 | 1579 | 1647 | 1864 | |

4.8% | 490 | 611 | 631 | 774 | 832 | 847 | 1043 | 1346 | 1612 | 1704 |

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**Figure 2.**Rainfall–runoff time series data in the study area (1995–2004): (

**a**) box and whisker plot with monthly distributions of rainfall; (

**b**) result of rainfall–runoff simulation.

**Figure 5.**A schematic diagram of the connection between a rainwater harvesting system simulation model and a particle swarm algorithm.

**Figure 6.**The capacity–reliability curves for the considered rainwater harvesting system: (

**a**) the capacity–temporal reliability curve; (

**b**) the capacity–volumetric reliability curve.

**Figure 7.**The results of the cost–benefit analysis for the capacity of the considered rainwater harvesting system: (

**a**) the capacity–BCR curve; (

**b**) the capacity–NPV curve.

**Figure 8.**The results of the cost–benefit analysis of the considered rainwater harvesting system without financial support programs: (

**a**) the capacity–BCR curve; (

**b**) the capacity–NPV curve.

**Figure 10.**The curves of fitted probability distributions and their 90% confidence intervals: (

**a**) histogram against the five distributions of the inflation rate; (

**b**) the normal distribution with a mean of 3.26 and a variance of 1.06 for the discount rate.

**Figure 11.**The results of the uncertainty analysis for the inflation rate: (

**a**) the maximum net present value; (

**b**) the corresponding capacity.

**Figure 12.**The results of our sensitivity analysis for the inflation and discount rates: (

**a**) the maximum net present value; (

**b**) the corresponding capacity.

**Table 1.**The costs and benefits of the installation and operation of rainwater harvesting systems (USD 1 = KRW 1300).

City | Financial Support and Billing Relief | |||
---|---|---|---|---|

Installation Costs | Water Utility Bill | |||

Water Supply Charge | Sewage Charge | Water Usage Charge | ||

Seoul | 90% of installation costs up to KRW 20 million (USD 15,384) | — | — | — |

Incheon | Full or partial support | 10% of RWU ^{1} | 10% of RWU | 10% of RWU |

Suwon | 90% of installation costs up to KRW 10 million (USD 7692) | Some RWU | Some RWU | Some RWU |

Sejong | Full or partial support | 10% of RWU | 30% of RWU | — |

Busan | 90% of installation costs up to KRW 10 million (USD 7692) | 10% of RWU | — | 10% of RWU |

^{1}RWU, rainwater usage.

**Table 2.**A water utility bill for 1000 ${\mathrm{m}}^{3}$ of water in Incheon, South Korea (USD 1 = KRW 1300).

Classification | Pricing Bracket | Unit Charge | Calculation Details |
---|---|---|---|

(${\mathbf{m}}^{3}$) | (KRW/${\mathbf{m}}^{3}$) | ||

Water Supply Charge | 1~300 | 870 (USD 0.67) | 300 ${\mathrm{m}}^{3}\phantom{\rule{3.33333pt}{0ex}}\times $ 870 KRW/${\mathrm{m}}^{3}$ = KRW 261,000 (USD 201) |

More than 300 | 1120 (USD 0.86) | 700 ${\mathrm{m}}^{3}\phantom{\rule{3.33333pt}{0ex}}\times $ 1120 KRW/${\mathrm{m}}^{3}$ = KRW 784,000 (USD 603) | |

Sewage Charge | 1~50 | 490 (USD 0.38) | 50 ${\mathrm{m}}^{3}\phantom{\rule{3.33333pt}{0ex}}\times $ 490 KRW/${\mathrm{m}}^{3}$ = KRW 24,500 (USD 18.8) |

51~100 | 510 (USD 0.39) | 50 ${\mathrm{m}}^{3}\phantom{\rule{3.33333pt}{0ex}}\times $ 510 KRW/${\mathrm{m}}^{3}$ = KRW 25,500 (USD 19.6) | |

101~300 | 1010 (USD 0.78) | 200 ${\mathrm{m}}^{3}\phantom{\rule{3.33333pt}{0ex}}\times $ 1010 KRW/${\mathrm{m}}^{3}$ = KRW 202,000 (USD 155) | |

301~500 | 1100 (USD 0.85) | 200 ${\mathrm{m}}^{3}\phantom{\rule{3.33333pt}{0ex}}\times $ 1100 KRW/${\mathrm{m}}^{3}$ = KRW 220,000 (USD 169) | |

501~1000 | 1130 (USD 0.87) | 500 ${\mathrm{m}}^{3}\phantom{\rule{3.33333pt}{0ex}}\times $ 1130 KRW/${\mathrm{m}}^{3}$ = KRW 565,000 (USD 435) | |

More than 1000 | 1160 (USD 0.89) | - | |

Water Usage Charge | Whole range | 170 (USD 0.13) | 1000 ${\mathrm{m}}^{3}\times $ 170 KRW/${\mathrm{m}}^{3}$ = KRW 170,000 (USD 131) |

Total Water Utility Bill | KRW 2,432,000 (USD 1871) |

**Table 3.**The costs and benefits of the installation and operation of a rainwater harvesting system (USD 1 = KRW 1300).

Classification | Category | Content | Remark | |
---|---|---|---|---|

Costs | Installation, construction, equipment, etc. | 350,000–450,000 KRW/${\mathrm{m}}^{3}$ (269–346 USD/${\mathrm{m}}^{3}$) | [44,45] | |

Maintenance expenses (labor, electricity, etc.) | 2% of installation costs | [44,45,46] | ||

Benefits | Savings on water utility bills by replacing water usage with rainwater usage | Equivalent to the amount of rainwater usage | See Table 1 | |

Subsidies for installation costs | Up to KRW 10 million (UDS 7692) | Full or partial support in Incheon, South Korea | ||

Water Utility Bill Concessions | Water supply charge concessions | 10% of water supply charges | Incheon, South Korea | |

Sewage charge concessions | 10% of sewage charges | |||

Water usage charge concessions | 10% of water usage charges |

Classification | Simulation Model | |
---|---|---|

Condition | Equation | |

Mass Balance Equation | — | $S{T}_{t}=S{T}_{t-1}+Q{F}_{t}-{Y}_{t}-EX{R}_{t}$ |

Yield Determination | $S{T}_{t-1}+Q{F}_{t}\ge T{D}_{t}$ | ${Y}_{t}=T{D}_{t}$ |

$S{T}_{t-1}+Q{F}_{t}\le T{D}_{t}$, and $S{T}_{t-1}\ne 0$ | ${Y}_{t}={S}_{t-1}$ | |

$S{T}_{t-1}+Q{F}_{t}\le T{D}_{t}$, and $S{T}_{t-1}=0$ | ${Y}_{t}=0$ | |

Spill Determination | ${S}_{t-1}+Q{F}_{t}-{Y}_{t}\ge Cap$ | $EX{R}_{t}=S{T}_{t-1}+Q{F}_{t}-{Y}_{t}-Cap$ |

${S}_{t-1}+Q{F}_{t}-{Y}_{t}<Cap$ | $EX{R}_{t}=0$ |

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**MDPI and ACS Style**

Jin, Y.; Lee, S.; Kang, T.; Park, J.; Kim, Y. Capacity Optimization of Rainwater Harvesting Systems Based on a Cost–Benefit Analysis: A Financial Support Program Review and Parametric Sensitivity Analysis. *Water* **2023**, *15*, 186.
https://doi.org/10.3390/w15010186

**AMA Style**

Jin Y, Lee S, Kang T, Park J, Kim Y. Capacity Optimization of Rainwater Harvesting Systems Based on a Cost–Benefit Analysis: A Financial Support Program Review and Parametric Sensitivity Analysis. *Water*. 2023; 15(1):186.
https://doi.org/10.3390/w15010186

**Chicago/Turabian Style**

Jin, Youngkyu, Sangho Lee, Taeuk Kang, Jongpyo Park, and Yeulwoo Kim. 2023. "Capacity Optimization of Rainwater Harvesting Systems Based on a Cost–Benefit Analysis: A Financial Support Program Review and Parametric Sensitivity Analysis" *Water* 15, no. 1: 186.
https://doi.org/10.3390/w15010186