# Developing Intensity-Duration-Frequency (IDF) Curves Based on Rainfall Cumulative Distribution Frequency (CDF) for Can Tho City, Vietnam

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

- Rainfall intensity (i, q), is the amount of rain falling per unit area in a unit of time. Rainfall intensity can be in the form of accumulative rainfall depth (i.e., mm/min, cm/h) or rainfall volume (q, L/s.ha) and is shown to be related by the formula q = 166.7i.
- Design rainfall time step (period, t), is the amount of rainfall in the calculation period (15 min or 30 min) assuming that the intensity does not change.
- Rainfall return period or frequency (N, years): is the time in years for the reappearance of rainfall of the equal amount (or greater than that of design intensity). The larger the rainfall, the less frequent it will occur (in case P ≤ 50%).

_{v}) suitable for rainfall in each period.

#### 2.1. Development of the IDF Rainfall Curve Using Empirical Formula

_{d}—rainfall duration (minutes); P, f (N)—rainfall event return period (year); A, C, b, n, q

_{20}—These parameters were determined according to local conditions ((Vietnamese standard TCVN 7975:2008; for areas not listed in the table, adjacent or the closest areas were used) [20].

#### 2.2. Selecting the Most Suitable IDF Rainfall Curve for Can Tho City

## 3. Results and Discussion

#### 3.1. Various Rainfall Intensity Duration Assessments

_{v}) for all periods was quite high (${C}_{v}\ge 0.2$), yet the fluctuations in the periods were found to be not significantly different from each other (C

_{v}ranges from 0.2 to 0.3) (Table 1). The high C

_{v}showed that the level of precipitation varied from period to period over the years. Although C

_{v}was quite high, the data series of 38 years for Can Tho station is quite long, so ${\sigma}_{\overline{x}}^{\prime}\le 6\%$ in all time periods. According to the Code of Calculation of Design Hydrological Characteristics (1997), the 38-year data series is reliable enough to represent the Can Tho station for calculating the cumulative rainfall frequency distribution. On the one hand, Figure 5 shows rainfall in the rainy season has tended to decrease, while on the other hand, the rainfall in the dry season has tended to increase. Rainfall in each period (15 min, 30 min, 60 min, 90 min, 120 min, and 180 min) has also tended to increase. Furthermore, rainfall over shorter periods has tended to increase, more than rainfall over longer periods. However, these uptrends showed low R-square values.

#### 3.2. Developing an IDF Rainfall Curve Based on CDF Rainfall Curve

#### 3.3. Development of IDF Rainfall Curve from Empirical Formulas According to the Vietnamese Standard (TCVN 7957:2008), the Department of Hydrology, and the Ministry of Transport

#### 3.4. The IDF Rainfall Built from Empirical Formulas That Have Been Used in Some Asian Countries

#### 3.5. Compareration the Selection of IDF Curves for the Study Area

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Figure A1.**Distribution curve of CDF various duration according to P.III. CDF rainfall curve of 15 min (

**a**), 30 min (

**b**), 60 min (

**c**), 90 min (

**d**), 120 min (

**e**), and 180 min (

**f**).

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**Figure 3.**Frequency curve of cumulative rainfall distribution, rainfall duration 60 min. TB denotes the average rainfall value, C

_{v}the denotes Coefficient of Variation, C

_{s}denotes the Coefficient of skewness.

**Figure 4.**Total rainfall in the wet season (from May to December) and in the dry season (from December to April) at Can Tho station.

**Figure 5.**The trend of maximum rainfall for 15 min (

**a**), 30 min (

**b**), 60 min (

**c**), 90 min (

**d**), 120 min (

**e**), 180 min (

**f**) periods, respectively.

**Figure 7.**Development of IDF rainfall curve based on the Viet Nam standard (TCVN 7957:2008, using the neighborhood parameter, Ca Mau province).

**Figure 8.**The IDF rainfall curve was built by the Department of Hydrology (

**a**) and the Ministry of Transport (

**b**).

**Figure 12.**Proposed IDF rainfall curve for Can Tho city. IDF curve proposed for Can Tho City with parameter modification, and IDF curve built from monitoring rainfall data of Can Tho City.

**Table 1.**Coefficient of variation and average relative error of maximum rainfall over each period at Can Tho station.

Rainfall Duration (Min) | C_{v} | ${\mathit{\sigma}}_{\overline{\mathit{x}}}^{\prime}=\frac{{\mathit{C}}_{\mathit{v}}}{\sqrt{\mathit{n}}}100\mathit{\%}\text{}(\%)$ | Rainfall Duration (Min) | C_{v} | ${\mathit{\sigma}}_{\overline{\mathit{x}}}^{\prime}=\frac{{\mathit{C}}_{\mathit{v}}}{\sqrt{\mathit{n}}}100\mathit{\%}\text{}(\%)$ |
---|---|---|---|---|---|

15 | 0.22 | 3.55 | 90 | 0.20 | 3.25 |

30 | 0.20 | 3.32 | 120 | 0.21 | 3.42 |

60 | 0.21 | 3.46 | 180 | 0.23 | 3.73 |

Return Period (N, year) | EI | RMSE | ||||
---|---|---|---|---|---|---|

Talbot | Kimijima | Bermard | Talbot | Kimijima | Bermard | |

2 year | 0.43 | 0.31 | 0.27 | 23.7 | 25.9 | 26.6 |

5 year | 0.70 | 0.64 | 0.54 | 21.1 | 22.9 | 26.0 |

10 year | 0.78 | 0.75 | 0.65 | 19.7 | 21.2 | 25.1 |

25 year | 0.83 | 0.82 | 0.74 | 19.9 | 20.8 | 25.0 |

50 year | 0.86 | 0.85 | 0.79 | 19.4 | 20.0 | 23.8 |

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**MDPI and ACS Style**

Minh, H.V.T.; Lavane, K.; Lanh, L.T.; Thinh, L.V.; Cong, N.P.; Ty, T.V.; Downes, N.K.; Kumar, P.
Developing Intensity-Duration-Frequency (IDF) Curves Based on Rainfall Cumulative Distribution Frequency (CDF) for Can Tho City, Vietnam. *Earth* **2022**, *3*, 866-880.
https://doi.org/10.3390/earth3030050

**AMA Style**

Minh HVT, Lavane K, Lanh LT, Thinh LV, Cong NP, Ty TV, Downes NK, Kumar P.
Developing Intensity-Duration-Frequency (IDF) Curves Based on Rainfall Cumulative Distribution Frequency (CDF) for Can Tho City, Vietnam. *Earth*. 2022; 3(3):866-880.
https://doi.org/10.3390/earth3030050

**Chicago/Turabian Style**

Minh, Huynh Vuong Thu, Kim Lavane, Le Thi Lanh, Lam Van Thinh, Nguyen Phuoc Cong, Tran Van Ty, Nigel K. Downes, and Pankaj Kumar.
2022. "Developing Intensity-Duration-Frequency (IDF) Curves Based on Rainfall Cumulative Distribution Frequency (CDF) for Can Tho City, Vietnam" *Earth* 3, no. 3: 866-880.
https://doi.org/10.3390/earth3030050