# Ranking of Storm Water Harvesting Sites Using Heuristic and Non-Heuristic Weighing Approaches

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Identification and Evaluation of Screening Parameters

- (i)
- Identification of hot spots,
- (ii)
- Estimation of runoff,
- (iii)
- Estimation of demand,
- (iv)
- Weighted demand distance.

#### 2.2. Normalization to a Common Scale

_{1}= α D

_{L}+ β,

_{2}= α D

_{U}+ β,

_{1}is lower value of range, D

_{2}is upper value of range, D

_{L}is lowest demand of the area, D

_{U}is highest demand of the area, and α and β are constants.

_{1}= γ RTD

_{L}+ δ,

_{2}= γ RTD

_{U}+ δ,

_{1}is lower value of the range, RTD

_{2}is upper value of the range, RTD

_{L}is lowest value of ratio of runoff to demand of the area, RTD

_{U}is the highest value of ratio of runoff to demand of the area, and γ and δ are constants.

_{1}= ζ WD

_{L}+ η,

_{2}= ζ WD

_{U}+ η,

_{1}is lower value of the range, WD

_{2}is upper value of the range, WD

_{L}is lowest value of inverse weighted demand distance of the area, and WD

_{U}is the highest value of inverse weighted demand distance of the area, ζ and η are constants.

_{1}to D

_{2}for demand, RTD

_{1}to RTD

_{2}for ratio of runoff to demand and WD

_{1}to WD

_{2}for inverse weighted demand distance by applying the following equations:

_{S}= α D

_{C}+ β,

_{S}= γ RTD

_{C}+ δ,

_{S}= ζ WD

_{C}+ η,

_{S}is scaled demand, D

_{C}is computed demand for each site, RTD

_{S}is scaled ratio of runoff to demand, RTD

_{C}is computed ratio of runoff to demand for each site, WD

_{S}is scaled inverse weighted distance and WD

_{C}is computed inverse weighted distance for each site.

#### 2.3. Determination of Weights

#### 2.3.1. Saaty Heuristic Approach

_{jk}represents the importance of j

^{th}criteria with respect to k

^{th}criteria.

_{norm}is formed, by making the sum equal to 1 of the all of the entries in the column of the matrix A, i.e., each entry $\mathrm{a}\prime $ of the matrix A

_{norm}is computed as

_{norm}, i.e.,

#### 2.3.2. Non-Heuristic Approaches

#### Principal Component Analysis (PCA) Method

^{n}or −λ

^{n}. It is a polynomial in λ of degree n.

#### Entropy Weight Method

_{ij})

_{mxn}, where x

_{ij}represents the actual value of j-th criteria for the i

^{th}parameter. The calculation of entropy weight is as follows.

_{ij})

_{mxn}where r

_{ij}is the j

^{th}evaluating object for i

^{th}indicator and r

_{ij}$\in $ [0,1]. This will in turn generate a positive indicator for the variables:

## 3. Case Study Application and Results

#### 3.1. Application of Methodology to Melbourne City

^{2}. Further SWH site specific details about Melbourne are elaborated [11]. The methodology is applied to Melbourne sites shortlisted for SWH. The set of data taken as shown in Table 1 is as follows. The ranking of sites according to high demand, high ratio of runoff to demand and low weighted distance had already been computed in the work.

#### 3.1.1. Saaty Heuristic Approach

#### 3.1.2. Non-Heuristic Method

#### Sites Ranked According to the PCA Method

#### Sites Ranked According to Entropy Weight Method

#### 3.2. Application of Methodology to Dehradun city

^{2}.

#### 3.2.1. Saaty Heuristic Approach

#### 3.2.2. Non-Heuristic Method

#### Sites Ranked According to the PCA Method

#### Sites Ranked According to Entropy Weight Method

## 4. Discussion

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Table 1.**Sites shortlisted for Storm Water Harvesting in Melbourne city [11].

Site ID | Possible Options | Demand (ML) | Ratio of Runoff to Demand | Weighted Distance (m) |
---|---|---|---|---|

76b | 49.07 | 1.3 | 300 | |

43c | 6.18 | 29.4 | 283 | |

43 | 43b | 5.82 | 31.2 | 277 |

46d | 7.47 | 14 | 256 | |

47d | 7.47 | 9.6 | 256 | |

44c | 6.43 | 62.6 | 255 | |

44 | 44b | 6.18 | 65.2 | 250 |

28 | 28b | 6.18 | 15.8 | 243 |

47c | 6.84 | 10.5 | 218 | |

46c | 6.84 | 15.3 | 217 | |

12 | 12b | 15.88 | 14.4 | 210 |

46 | 46b | 5.82 | 18 | 182 |

47 | 47b | 5.82 | 12.4 | 182 |

14 | 14b | 125.6 | 1.8 | 182 |

69 | 69b | 11.62 | 81.6 | 175 |

29d | 31.65 | 4.2 | 136 | |

52b | 13.7 | 8.5 | 134 | |

17d | 53.79 | 1.3 | 112 | |

41d | 30.65 | 2.2 | 103 | |

26 | 26b | 19.35 | 2.6 | 87 |

39 | 39b | 19.35 | 1.6 | 87 |

29c | 28.92 | 4.6 | 80 | |

78b | 13.07 | 1.5 | 70 | |

41c | 28.92 | 2.3 | 67 | |

52 | 52a | 5.33 | 21.9 | 0 |

76 | 76a | 5.3 | 11.8 | 0 |

29 | 29a | 23.14 | 5.8 | 0 |

78 | 78a | 5.3 | 3.7 | 0 |

77 | 77a | 5.3 | 3.2 | 0 |

17 | 17a | 23.14 | 3 | 0 |

41 | 41a | 23.14 | 2.9 | 0 |

20 | 20a | 23.14 | 2.8 | 0 |

9 | 9b | 28.67 | 1.3 | 0 |

Rank | Possible Options | Scaled Demand | Scaled Inverse WD | Scaled RTD | Centroid (m) |
---|---|---|---|---|---|

10 Intercept | 5 Intercept | 0 Intercept | |||

1 | 69b | 5.25 | 20.81 | 100.00 | 42.0 |

2 | 41c | 19.63 | 100.22 | 1.25 | 40.4 |

3 | 14b | 100.00 | 18.92 | 0.62 | 39.8 |

4 | 29c | 19.63 | 79.31 | 4.11 | 34.4 |

5 | 78b | 6.46 | 94.70 | 0.25 | 33.8 |

6 | 17d | 40.31 | 48.52 | 0.00 | 29.6 |

7 | 44b | 0.73 | 6.03 | 79.57 | 28.8 |

8 | 26b | 11.68 | 70.64 | 1.62 | 28.0 |

9 | 39b | 11.68 | 70.64 | 0.37 | 27.6 |

10 | 44c | 0.94 | 5.36 | 76.34 | 27.5 |

11 | 41d | 21.07 | 55.25 | 1.12 | 25.8 |

12 | 29d | 21.90 | 34.94 | 3.61 | 20.2 |

13 | 52b | 6.98 | 35.89 | 8.97 | 17.3 |

14 | 43b | 0.43 | 2.67 | 37.23 | 13.4 |

15 | 46b | 0.43 | 18.92 | 20.80 | 13.4 |

Rank | Possible Options | Scaled Demand | Scaled RTD | Center Point (m) |
---|---|---|---|---|

10 Intercept | 0 Intercept | |||

1 | 52a | 0.02 | 25.65 | 12.84 |

2 | 29a | 14.83 | 5.6 | 10.22 |

3 | 9b | 19.43 | 0 | 9.71 |

4 | 17a | 14.83 | 2.12 | 8.47 |

5 | 41a | 14.83 | 1.99 | 8.41 |

Rank | Saaty AHP Method | Entropy Weight Method | PCA Method |
---|---|---|---|

1 | 69b | 14b | 69b |

2 | 41c | 69b | 44b |

3 | 14b | 41c | 44c |

4 | 29c | 44b | 41c |

5 | 78b | 44c | 29c |

6 | 17d | 17d | 78b |

7 | 44b | 29c | 43b |

8 | 26b | 78b | 43c |

9 | 39b | 41d | 26b |

10 | 44c | 26b | 14b |

11 | 41d | 39b | 39b |

12 | 29d | 29d | 17d |

13 | 52b | 76b | 41d |

14 | 43b | 52b | 46b |

15 | 46b | 43b | 52b |

16 | 43c | 43c | 29d |

17 | 12b | 12b | 12b |

18 | 76b | 46b | 46c |

19 | 47b | 47b | 47b |

20 | 46c | 46c | 28b |

ID | Radius of Influence (RI) (m) | Total Area (m^{2}) | Urban Area (m^{2}) | Urban Runoff Volume (ML) (Monthly) | Water Demand (ML) (Monthly) | Ratio of Runoff to Demand | Weighted Distance |
---|---|---|---|---|---|---|---|

A | 200 | 125,663.7 | 93,765 | 39.3 | 4.5 | 8.8 | 4.2 |

A | 400 | 502,654.8 | 313,553 | 157.4 | 15 | 10.5 | 9.6 |

A | 600 | 1,130,973 | 534,297.6 | 354.1 | 25.5 | 13.9 | 15.9 |

A | 800 | 2,010,619 | 956,866.5 | 629.5 | 45.7 | 13.8 | 19.7 |

A | 1000 | 3,141,593 | 1,443,163 | 983.6 | 68.9 | 14.3 | 25 |

B | 200 | 125,663.7 | 4915 | 39.3 | 0.2 | 167.6 | 8.1 |

B | 400 | 502,654.8 | 108,944.4 | 157.4 | 5.2 | 30.2 | 13.4 |

B | 600 | 1,130,973 | 465,995 | 354.1 | 22.3 | 15.9 | 20.4 |

B | 800 | 2,010,619 | 982,995 | 629.5 | 46.9 | 13.4 | 26.1 |

B | 1000 | 3,141,593 | 1,770,438 | 983.6 | 84.6 | 11.6 | 28.1 |

C | 200 | 125,663.7 | 62,829.9 | 39.3 | 3 | 13.1 | 6.3 |

C | 400 | 502,654.8 | 170,539.4 | 157.4 | 8.1 | 19.3 | 11.6 |

C | 600 | 1,130,973 | 309,677 | 354.1 | 14.8 | 23.9 | 16 |

C | 800 | 2,010,619 | 495,541.5 | 629.5 | 23.7 | 26.6 | 25.5 |

C | 1000 | 3,141,593 | 831,424 | 983.6 | 39.7 | 24.8 | 28.7 |

D | 200 | 125,663.7 | 11,413 | 39.3 | 0.5 | 72.2 | 141.2 |

D | 400 | 502,654.8 | 29,059.4 | 157.4 | 1.4 | 113.4 | 13 |

D | 600 | 1,130,973 | 87,418.9 | 354.1 | 4.2 | 84.8 | 19.4 |

D | 800 | 2,010,619 | 251,187.5 | 629.5 | 12 | 52.5 | 28.9 |

D | 1000 | 3,141,593 | 738,246 | 983.6 | 35.3 | 27.9 | 36.8 |

E | 200 | 125,663.7 | 36,676 | 39.3 | 1.8 | 22.5 | 6.5 |

E | 400 | 502,654.8 | 205,243 | 157.4 | 9.8 | 16.1 | 9.9 |

E | 600 | 1,130,973 | 309,245 | 354.1 | 14.8 | 24 | 11.7 |

E | 800 | 2,010,619 | 420,560 | 629.5 | 20.1 | 31.3 | 18 |

E | 1000 | 3,141,593 | 557,655 | 983.6 | 26.6 | 36.9 | 22.6 |

F | 200 | 125,663.7 | 9102 | 39.3 | 0.4 | 90.5 | 139.5 |

F | 400 | 502,654.8 | 180,030 | 157.4 | 8.6 | 18.3 | 13 |

F | 600 | 1,130,973 | 537,586 | 354.1 | 25.7 | 13.8 | 15 |

F | 800 | 2,010,619 | 1,005,158 | 629.5 | 48 | 13.1 | 20.7 |

F | 1000 | 3,141,593 | 1,741,692 | 983.6 | 83.2 | 11.8 | 29.7 |

G | 200 | 125,663.7 | 58,561.5 | 39.3 | 2.8 | 14.1 | 2.2 |

G | 400 | 502,654.8 | 218,306.4 | 157.4 | 10.4 | 15.1 | 8.9 |

G | 600 | 1,130,973 | 619,860 | 354.1 | 29.6 | 12 | 9.5 |

G | 800 | 2,010,619 | 1,192,337 | 629.5 | 56.9 | 11.1 | 12.9 |

G | 1000 | 3,141,593 | 1,932,770 | 983.6 | 92.3 | 10.7 | 17 |

H | 200 | 125,663.7 | 31,584.1 | 39.3 | 1.5 | 26.1 | 5.8 |

H | 400 | 502,654.8 | 245,109.6 | 157.4 | 11.7 | 13.4 | 8.5 |

H | 600 | 1,130,973 | 587,960.8 | 354.1 | 28.1 | 12.6 | 10.9 |

H | 800 | 2,010,619 | 1,026,758 | 629.5 | 49 | 12.8 | 18.1 |

H | 1000 | 3,141,593 | 1,572,652 | 983.6 | 75.1 | 13.1 | 22.7 |

Rank | Saaty AHP Method | Entropy Weight Method | PCA Method | |||
---|---|---|---|---|---|---|

ID | RI (m) | ID | RI (m) | ID | RI (m) | |

1 | B | 200 | B | 200 | B | 200 |

2 | G | 1000 | D | 400 | D | 400 |

3 | G | 200 | G | 200 | D | 600 |

4 | B | 1000 | G | 1000 | G | 200 |

5 | F | 1000 | D | 600 | D | 800 |

6 | H | 1000 | B | 1000 | E | 1000 |

7 | A | 1000 | F | 1000 | H | 200 |

8 | D | 400 | H | 1000 | G | 1000 |

9 | G | 800 | A | 1000 | E | 800 |

10 | H | 800 | G | 800 | E | 200 |

11 | F | 800 | D | 800 | A | 200 |

12 | A | 800 | E | 1000 | B | 1000 |

13 | D | 600 | H | 800 | H | 1000 |

14 | B | 800 | C | 1000 | F | 1000 |

15 | C | 1000 | A | 200 | D | 1000 |

16 | A | 200 | H | 200 | B | 400 |

17 | G | 600 | F | 800 | C | 1000 |

18 | E | 1000 | A | 800 | A | 1000 |

19 | D | 1000 | D | 1000 | E | 600 |

20 | H | 600 | B | 800 | G | 800 |

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**MDPI and ACS Style**

Pathak, S.; Ojha, C.S.P.; Zevenbergen, C.; Garg, R.D.
Ranking of Storm Water Harvesting Sites Using Heuristic and Non-Heuristic Weighing Approaches. *Water* **2017**, *9*, 710.
https://doi.org/10.3390/w9090710

**AMA Style**

Pathak S, Ojha CSP, Zevenbergen C, Garg RD.
Ranking of Storm Water Harvesting Sites Using Heuristic and Non-Heuristic Weighing Approaches. *Water*. 2017; 9(9):710.
https://doi.org/10.3390/w9090710

**Chicago/Turabian Style**

Pathak, Shray, Chandra Shekhar Prasad Ojha, Chris Zevenbergen, and Rahul Dev Garg.
2017. "Ranking of Storm Water Harvesting Sites Using Heuristic and Non-Heuristic Weighing Approaches" *Water* 9, no. 9: 710.
https://doi.org/10.3390/w9090710