# A 60-Minute Design Rainstorm for the Urban Area of Yangpu District, Shanghai, China

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

^{2}, Yen and Chow [16] proposed a triangular-shaped hyetograph. The position of the peak is determined by the dimensionless first-order moment of the rainstorm event. The Natural Resources Conservation Service (NRCS) [17] developed a synthetic hyetograph, utilizing 6 h and 24 h rainstorm data from the US, which is called a “Soil Conservation Service (SCS) hyetograph”. There are four basic types of SCS hyetographs, each of them accounting for a specific region and climate. Besides the above-mentioned classic methods, there are also newly-developed methods to derive hyetographs; refer to Cheng et al. [18], Lin and Wu [19], Powell et al. [20], Lee and Ho [21], and Kottegoda [22] for detailed descriptions.

## 2. Materials and Methods

#### 2.1. Study Area

^{2}. The Huangpu River winds along the southeast side of the district. The subtropical monsoon climate results in an average annual precipitation of 1060 mm.

#### 2.2. Process of Precipitation Data

#### 2.3. Overall Procedure

- Calculation of the areal rainfall in Yangpu District using the arithmetic average method.
- Frequency analysis using Pearson-III distribution in order to derive the maximum 60-min areal rainfall with return periods of 2, 5, 10, and 20 years.
- Classification of rainfall events into seven types of mode hyetographs using the fuzzy identification method.
- Use the P&C method to derive single-peak hyetographs and double-peak hyetographs.

#### 2.4. Areal Rainfall Estimation

#### 2.5. Frequency Analysis

_{s}, and C

_{v}were estimated by the L-moment method [33]. They can be expressed as follows:

_{s}, and C

_{v}can be expressed by:

_{1}, l

_{2}, l

_{3}, and ${\tau}_{3}$ (${\tau}_{3}$ = l

_{2}/l

_{3}) can be found in Hosking and Wallis [33].

_{m}is the empirical probability for the mth term of the sequence, and n is the length of the sequence.

#### 2.6. Fuzzy Identification to Classify Hyetograph

_{i}is the rainfall in the ith period, and H is the total rainfall.

_{i}is defined as the actual rainfall indices, denoted as vector X:

_{k}:

_{ki}is computed in the same way as x

_{i}.

_{ki}.

#### 2.7. Pilgrim and Cordery Method

- Each rainfall event is divided into n periods by certain time intervals, and the percentage of the rainfall in each period is computed.
- The periods are sorted in descending order according to the percentage of the rainfall, and for each period, the average rank of all the rainfall events is computed as the rank for this period.
- For all the rainfall events, the average percentage of the rainfall in the periods of the same rank is computed.
- For each period, the rank and the percentage of the rainfall are paired to obtain the temporal distribution of the rainfall process.
- The hyetograph can be obtained by multiplying the percentage of the rainfall in each period by the design rainstorm amount with a given return period.

- Scenario 1: Single-peak hyetograph (Type I, II, III);
- Scenario 2: Double-peak hyetograph (Type V, VI, VII);
- Scenario 3: General hyetograph (excluding Type IV).

#### 2.8. The Chicago Rainstorm Method

## 3. Results and Discussion

## 4. Conclusions and Recommendations

- The result of the classification of the 117 rainstorm events indicates that single-peak hyetographs account for about 60% of these events, compared to double-peak hyetographs which account for about 30%. The rest are uniformly distributed hyetographs.
- Both the single-peak and double-peak hyetographs are smooth and rational. The general hyetograph is irrational due to its relatively even and disordered distribution of rainfall amount.
- The design rainstorm using the proposed methodology in this study shows superiority to the classic Chicago rainstorm method. On one hand, it can derive both single-peak and double-peak hyetographs. On the other hand, it is more disadvantageous as input to runoff models.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 1.**Location of Yangpu District. Triangles denote rain gauges whose data are used in the study.

**Figure 6.**Rainfall distribution of the design hyetograph for scenario 3: combining single-peak and double-peak rainstorms.

**Figure 7.**The 60-min design hyetograph with a 20-year return period using Chicago rainstorm method and P&C method (single-peak). The blue bar denotes the Chicago hyetograph and the orange bar denotes the P&C hyetograph.

Return Period/a | Design Areal Rainfall Amount/mm |
---|---|

2 | 46 |

5 | 63 |

10 | 73 |

20 | 83 |

Type | Events | Percentage/% |
---|---|---|

I | 19 | 16.24 |

II | 20 | 17.09 |

III | 30 | 25.64 |

IV | 14 | 11.97 |

V | 17 | 14.53 |

VI | 11 | 9.40 |

VII | 6 | 5.13 |

**Table 3.**Rainfall allocation of a single-peak rainstorm with a 60-min duration and a 20-year return period in Yangpu District.

Time/min | Percentage of Rainfall/% | Rainfall Amount/mm | Cumulative Rainfall Amount/mm |
---|---|---|---|

5 | 0.81 | 0.67 | 0.67 |

10 | 3.76 | 3.10 | 3.77 |

15 | 11.03 | 9.10 | 12.87 |

20 | 14.69 | 12.12 | 24.99 |

25 | 25.25 | 20.83 | 45.83 |

30 | 18.72 | 15.45 | 61.27 |

35 | 7.99 | 6.59 | 67.86 |

40 | 6.10 | 5.03 | 72.90 |

45 | 4.84 | 3.99 | 76.89 |

50 | 2.93 | 2.42 | 79.31 |

55 | 2.35 | 1.94 | 81.25 |

60 | 1.55 | 1.28 | 82.51 |

**Table 4.**Rainfall allocation of double-peak rainstorm with a 60-min duration and a 20-year return period in Yangpu District.

Time/min | Percentage of Rainfall/% | Rainfall Amount/mm | Cumulative Rainfall Amount/mm |
---|---|---|---|

5 | 3.19 | 2.63 | 2.63 |

10 | 16.71 | 13.79 | 16.42 |

15 | 8.74 | 7.21 | 23.63 |

20 | 1.52 | 1.25 | 24.89 |

25 | 2.27 | 1.87 | 26.76 |

30 | 4.02 | 3.32 | 30.07 |

35 | 5.89 | 4.86 | 34.93 |

40 | 22.68 | 18.71 | 53.65 |

45 | 10.51 | 8.67 | 62.32 |

50 | 12.76 | 10.53 | 72.85 |

55 | 7.05 | 5.82 | 78.67 |

60 | 4.68 | 3.86 | 82.51 |

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**MDPI and ACS Style**

Wang, A.; Qu, N.; Chen, Y.; Li, Q.; Gu, S.
A 60-Minute Design Rainstorm for the Urban Area of Yangpu District, Shanghai, China. *Water* **2018**, *10*, 312.
https://doi.org/10.3390/w10030312

**AMA Style**

Wang A, Qu N, Chen Y, Li Q, Gu S.
A 60-Minute Design Rainstorm for the Urban Area of Yangpu District, Shanghai, China. *Water*. 2018; 10(3):312.
https://doi.org/10.3390/w10030312

**Chicago/Turabian Style**

Wang, Anqi, Ningling Qu, Yuanfang Chen, Qi Li, and Shenghua Gu.
2018. "A 60-Minute Design Rainstorm for the Urban Area of Yangpu District, Shanghai, China" *Water* 10, no. 3: 312.
https://doi.org/10.3390/w10030312