# The Life cycle Assessment Integrated with the Lexicographic Method for the Multi-Objective Optimization of Community-Based Rainwater Utilization

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

_{V}= 0.633) with variations in the floor area ratio, total runoff coefficient and reservoir volume. Changes in the total runoff coefficient were the main source of the uncertainty, which suggested that more attention should be paid to the area ratio of each underlying surface. In addition, economic support from the government is urgently required for the further promotion and development of CB-RWU.

## 1. Introduction

## 2. Methods

#### 2.1. Study Area

^{2}, with a population of 90,000, including 68,000 residents and 22,000 villagers. Figure 1 presents the location and land use type of Dadeng Island. A reservoir of flood-regulating lakes is around the island, with a total water area of 1.18 km

^{2}.

#### 2.2. LCA Model

#### 2.2.1. Rainwater Utilization Mode

#### 2.2.2. Goal and Scope

^{3}of water supply. All the relevant data, including the durable years, data on rainfall, the consumption of raw materials, chemicals, fossil energy, electric energy, etc., and the discharge of air, water and solid pollutants during the CB-RWU process were collected from the Meteorological Bureau, related standards for rainwater utilization and previous studies [17,45,46,47,48].

#### 2.2.3. Inventory Analysis

^{3}, respectively. A total of 80 sets of CB-RWU scenarios with different FAR (1, 1.7, 2.4 and 3.1), total runoff coefficients (0.09, 0.20, 0.31 and 0.42) and reservoir volume (33FAR, 66FAR, 99FAR, 132FAR and 165FAR) were simulated, and a life cycle assessment model was established to analyze the impact of changes in these three factors during the whole life cycle on the environment. Table S1 in Supplementary Materials reports the engineering quantity list.

#### 2.2.4. Life Cycle Impact Assessment

#### 2.3. Multi-Objective Optimization Model

#### 2.3.1. Object Functions

_{i}(m

^{3}) denotes the conventional water resources saved using rainwater in year i; P

_{i}(CNY/m

^{3}) is the price of conventional water resources in year i, which was valued as 3.2 CNY/m

^{3}in the study aera [49]; I

_{i}(CNY) is the investment of the CB-RWU system in year i (e.g., material, installation, on-site construction and material transportation costs); M

_{i}(CNY) is the O&M costs in year i (e.g., electricity, equipment replacement and maintenance costs) [50]; r is the annual interest rate and was valued at 4.06% [51], and T is the total years of operation and was valued at 30 years [52,53]. The electricity price in the study area was 0.667 CNY/kw·h, and other costs were estimated according to the Investment Estimate Index of Sponge City Construction Project (ZYA1-02(01)-2018).

_{C}(m

^{3}) is the volume of the underground reservoir, and Ψ is the total runoff coefficient of the community, which can be expressed as:

_{k}is the runoff coefficient for each underlying surface, the range of which is from the technical code for rainwater management and utilization of building and subdistrict (GB50400-2016) and previous studies [54,55] and shown in Table 2; and β

_{k}is the proportion of area for each underlying surface to the total catchment area. According to the standard for urban residential area planning and design (GB50180-2018), β

_{3}and β

_{4}were set as 0.1 and 0.25, respectively, while β

_{1}and β

_{2}ranged between 0 to 0.65, and δ

_{k}is the abandoned flow at the beginning of rainfall. According to the standard (GB50400-2016), δ

_{1}-δ

_{3}was set as 5 mm and δ

_{4}as 2 mm; H

_{t}is the rainfall on day t and was determined using average daily rainfall data for 30 years (1980–2009); and F (m

^{2}) is the total area of the catchment area, valued as 30,000 m

^{2}.

_{t}(m

^{3}) is the water used on day t, and D

_{t}(m

^{3}) is the non-potable water demand (e.g., toilet flushing and other indoor uses) on day t, calculated using Equations (6)–(9):

_{t}(m

^{3}) is the remaining rainfall in the reservoir at the end of day t; n (L/per

^{−1}·d

^{−1}) is the daily water use quota of the study area, taken as 160 L/per

^{−1}·d

^{−1}based on the norm of industrial water use and living water use (DB3502/Z 5016-2016); d is the number of days which CB-RWU is running, taken as 1 day; α is the proportion of non-potable water in the daily water use quota, which was set as 40% based on the standard for design of building reclaimed water system (GB50036-2002); and N is the population of the community and was calculated as:

#### 2.3.2. Constraints

^{3}, and the remaining rainfall was always greater than or equal to 0 m

^{3}. The volume of the underground reservoir was less than three times the daily demand. The total area of the four underlying surfaces was equal to the total design catchment area, namely, 30,000 m

^{2}. The FAR of the residential community was between 1 and 3.1.

#### 2.3.3. Datasets

#### 2.3.4. Lexicographic Method

- Determine the sequence of objective functions. The first-level goal was to maximum the BCR; the second-level goal was to maximum the WSE; and the third-level goal was to minimize the ADPF.
- First-level optimization. Solve the optimization model with the maximization of the BCR as the goal under the initial constraints, obtaining a solution set and the maximum BCR.
- Second-level optimization. Modify the constraints and solve the optimization model with the maximization of the WSE as the goal within the first-level optimal solution range, obtaining a solution set and the maximum WSE.
- Third-level optimization. Modify the constraints and solve the optimization model with the minimization of the ADPF as the goal within the second-level optimal solution range, obtaining a solution set and the minimum ADPF.
- Check the solutions of the total runoff coefficient, reservoir volume and FAR. Stop the calculation and output the final optimal solution of the model.

#### 2.4. Uncertainty Analysis

#### 2.4.1. Sources of Uncertainty

#### 2.4.2. Monte Carlo Analysis

## 3. Results and Discussion

#### 3.1. LCA Performance Analysis of CB-RWU

^{3}) was much lower than the empirical energy consumption (median 1.40 kWh/m

^{3}). On the one hand, this result indicated that part of the energy consumption in the system may be ignored in the theoretical analysis; on the other hand, it also indicated a large optimization space of the current rainwater utilization system [66]. Therefore, eliminating or reducing pumping energy was key to reducing the environmental impacts of CB-RWU. For example, an alternate energy mix could minimize impacts of a dominant release contributor.

^{2}and the root mean squared error RMSE were equal to 0.8751 and 19.967, respectively, indicating the excellent fitting effect.

#### 3.2. Multi-Objective Optimization of CB-RWU

#### 3.3. Uncertainty Analysis

_{V}) was used to describe the degree of dispersion of a set of data. The greater the degree of dispersion, the higher the uncertainty of the simulated objective function [71]. The C

_{V}of the BCR was the lowest (0.395) among the three objective functions, while that of the ADPF was the highest (0.633). This is consistent with the trend shown in Figure 6. Thus, the uncertainty of the environmental impact was the highest with variations in the FAR, total runoff coefficient and reservoir volume, followed by WSE and BCR.

_{V}obtained from the Monte Carlo simulation (ADPF > WSE > BCR), indicating that the higher the uncertainty of the objective function, the larger the underestimation/overestimation deviation of the benefits.

_{V}of the BCR was consistently lower than the other two objective functions, indicating that it exhibited the lowest uncertainty from changes in the three parameters. The changes in the FAR and reservoir volume had a minimal impact on the uncertainty of the WSE and environmental impact, while changes in the total runoff coefficient had a far greater impact on the environmental benefits compared to the water resource benefits. Quantitative analysis of the uncertainty sources was then conducted (Figure 7). The uncertainty of the three objective functions mainly originated from changes in the total runoff coefficient, with a relative contribution rate of 80.0%, 68.5% and 84.4% for BCR, WSE and ADPF, respectively. Changes in the FAR and total runoff coefficient had the greatest impact on the uncertainty of environmental impact, while changes in the reservoir volume had the greatest impact on the WSE.

## 4. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

ADP elements | abiotic depletion potential elements, kg Sb eq. |

ADPF | abiotic depletion potential for fossil fuels, MJ |

AP | acidification potential, kg SO_{2} eq. |

BCR | benefit–cost ratio |

CB-RWU | community-based rainwater utilization |

COD | chemical oxygen demand |

C_{V} | coefficient of variance |

d | days of community-based rainwater utilization runed |

D_{t} | water demand on day t, m^{3} |

EP | eutrophication potential, kg PO_{4}^{3−} eq. |

F | the total area of the catchment area, m^{2} |

FAETP | freshwater aquatic ecotoxicity potential, kg DCB eq. |

FAR | floor area ratio |

GHG | greenhouse gas |

GWP | global warming potential, kg CO_{2} eq. |

H_{t} | the rainfall on day t, mm |

HTP | human toxicity potential, kg DCB eq. |

I_{i} | investment of community-based rainwater utilization system in year i, yuan |

ISO | International Organization for Standardization |

${\mathrm{I}}_{{\mathrm{t}}_{\mathrm{k}}}$ | runoff generated on day t |

k | the underlying surface types, namely, green land (k = 1), permeable pavement (k = 2), hard pavement (k = 3) and roof (k = 4) |

LCA | life cycle assessment |

LID | low-impact development |

MAETP | marine aquatic ecotoxicity potential, kg DCB eq. |

Mi | the operation and maintenance costs in year i, yuan |

n | the daily water used quota of the study aera, L/per^{−1}·d^{−1} |

N | the population of the community |

NSGA-II | the nondominated sorting genetic algorithm II |

O&M | the operation and maintenance |

P_{i} | price of conventional water resources in year i, yuan/m^{3} |

POCP | photochemical ozone creation potential, kg Ethene eq. |

r | annual interest rate |

RMSE | root mean square error |

R_{t} | the remaining rainfall in the reservoir at the end of day t, m^{3} |

RWH | rainwater harvesting |

S_{C} | storage capacity, m^{3} |

S_{i} | conventional water resources saved by using rainwater in year i, m^{3} |

SS | suspended solids |

T | total years of operation, y |

TETP | terrestrial ecotoxicity potential, kg DCB eq. |

WSE | water-saving efficiency |

Y_{t} | water used on day t, m^{3} |

α | the proportion of non-potable water in the daily water use quota |

β_{k} | the proportion of area for each underlying surface to total catchment area |

δ_{k} | the abandoned flow at the beginning of rainfall, mm |

Ψ | the total runoff coefficient of the community |

Ψ_{k} | the runoff coefficient of each underlying surface |

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**Figure 2.**System boundary of rainwater harvesting and utilization for the life cycle assessment study.

**Figure 3.**Methodology flowchart for multi-objective optimization of rainwater harvesting and utilization.

**Figure 4.**Life cycle assessment results of community-based rainwater utilization when the floor area ratio was: (

**a**) 1; (

**b**) 1.7; (

**c**) 2.4; (

**d**) 3.1. (EP: eutrophication potential; FAETP: freshwater aquatic ecotoxicity potential; POCP: photochemical ozone creation potential; ADP elements: abiotic depletion potential elements; AP: acidification potential; TETP: terrestrial ecotoxicity potential: global warming potential; HTP: human toxicity potential; ADPF: abiotic depletion potential for fossil fuels; MAETP: marine aquatic ecotoxicity potential).

**Figure 5.**Normalization results of community-based rainwater utilization. (EP: eutrophication potential; FAETP: freshwater aquatic ecotoxicity potential; POCP: photochemical ozone creation potential; ADP elements: abiotic depletion potential elements; AP: acidification potential; TETP: terrestrial ecotoxicity potential: global warming potential; HTP: human toxicity potential; ADPF: abiotic depletion potential for fossil fuels; MAETP: marine aquatic ecotoxicity potential).

**Figure 6.**Simulated values histogram of: (

**a**) benefit–cost ratio; (

**b**) water-saving efficiency; (

**c**) abiotic depletion potential for fossil fuels.

Category | Indicators | Abbreviation | Unit |
---|---|---|---|

Resource depletion | Abiotic Depletion Potential for fossil fuels | ADPF | MJ |

Abiotic Depletion Potential elements | ADP elements | kg Sb eq. | |

Ecosystem | Acidification Potential | AP | kg SO_{2} eq. |

Eutrophication Potential | EP | kg PO_{4}^{3−} eq. | |

Marine Aquatic Ecotoxicity Potential | MAETP | kg DCB eq. | |

Freshwater Aquatic Ecotoxicity Potential | FAETP | kg DCB eq. | |

Terrestrial Ecotoxicity Potential | TETP | kg DCB eq. | |

Human health | Global Warming Potential | GWP | kg CO_{2} eq. |

Human Toxicity Potential | HTP | kg DCB eq. | |

Photochemical Oxidant Creation Potential | POCP | kg Ethene eq. |

Number | Underlying Surface Type | Runoff Coefficient (Ψ_{k}) |
---|---|---|

1 | Green lands | 0.15 |

2 | Permeable pavement | 0.29–0.36 |

3 | Hard pavement | 0.80–0.90 |

4 | Roof | 0.60–0.70 |

Parameters | Probability Distribution | Range | Mathematical Expectation |
---|---|---|---|

Total runoff coefficient | Normal distribution | [0.09, 0.42] | 0.255 |

Reservoir volume (m^{3}) | Minimum distribution | [33, 500] | 270.6 |

Floor area ratio (FAR) | Normal distribution | [1.0, 3.1] | 2.05 |

Benefit–Cost Ratio | Water-Saving Efficiency | Abiotic Depletion Potential for Fossil Fuels (MJ) | Floor Area Ratio | Total Runoff Coefficient | Reservoir Volume (m^{3}) | |
---|---|---|---|---|---|---|

Lexicographic optimization with benefit–cost ratio prioritized above water-saving efficiency and environmental impact | ||||||

The first-level | 0.3347 | 32.71% * | 26.31 * | 1.000 | 0.420 | 165 |

The second-level | 0.3288 | 31.63% | 29.24 * | 1.070 | 0.415 | 172 |

The third-level | 0.3098 | 28.47% | 24.68 | 1.017 | 0.420 | 124 |

Lexicographic optimization with environmental impact prioritized above water-saving efficiency and benefit–cost ratio | ||||||

The first-level | 0.2456 | 19.84% | 21.56 | 1.000 | 0.420 | 33 |

The second-level | 0.3091 | 28.36% | 24.63 | 1.000 | 0.420 | 118 |

The third-level | 0.3029 | 27.45% | 24.38 | 1.003 | 0.420 | 110 |

Traditional multi-objective optimization | ||||||

/ | 0.2456 | 19.84% | 21.56 | 1.000 | 0.420 | 33 |

Number | Underlying Surface Type | Runoff Coefficient (Ψ_{k}) | Proportion of Area (β_{k}) |
---|---|---|---|

1 | green lands | 0.15 | 35% |

2 | Permeable pavement | 0.36 | 30% |

3 | Hard pavement | 0.90 | 10% |

4 | Roof | 0.70 | 25% |

Objective Functions | Average Input ^{1} | Average ^{2} | Standard Deviation ^{2} | Coefficient of Variation (C _{V}) ^{2} |
---|---|---|---|---|

Benefit-cost ratio | 0.217 | 0.238 | 0.094 | 0.395 |

Water-saving efficiency | 18.5% | 20.5% | 0.089 | 0.433 |

Abiotic depletion potential for fossil fuels | 92.5 MJ | 118.8 MJ | 75.222 MJ | 0.633 |

^{1}The results were calculated by using the average of each parameter.

^{2}The results were calculated by the Monte Carlo simulation.

Coefficient of Variation (C_{V}) | Benefit–Cost Ratio (BCR) | Water-Saving Efficiency (WSE) | Abiotic Depletion Potential for Fossil Fuels (ADPF) |
---|---|---|---|

Floor-area ratio (FAR) | 0.078 | 0.124 | 0.178 |

Total runoff coefficient | 0.661 | 0.664 | 1.620 |

Reservoir volume | 0.087 | 0.182 | 0.121 |

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© 2023 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 (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Li, Y.; Xu, W.; Zhang, W.; Huang, Y.; Wan, F.; Xiong, W. The Life cycle Assessment Integrated with the Lexicographic Method for the Multi-Objective Optimization of Community-Based Rainwater Utilization. *Int. J. Environ. Res. Public Health* **2023**, *20*, 2183.
https://doi.org/10.3390/ijerph20032183

**AMA Style**

Li Y, Xu W, Zhang W, Huang Y, Wan F, Xiong W. The Life cycle Assessment Integrated with the Lexicographic Method for the Multi-Objective Optimization of Community-Based Rainwater Utilization. *International Journal of Environmental Research and Public Health*. 2023; 20(3):2183.
https://doi.org/10.3390/ijerph20032183

**Chicago/Turabian Style**

Li, Yi, Wenjun Xu, Wenlong Zhang, Youyi Huang, Fenfen Wan, and Wei Xiong. 2023. "The Life cycle Assessment Integrated with the Lexicographic Method for the Multi-Objective Optimization of Community-Based Rainwater Utilization" *International Journal of Environmental Research and Public Health* 20, no. 3: 2183.
https://doi.org/10.3390/ijerph20032183