# Application of the HEC-RAS Program in the Simulation of the Streamflow Hydrograph for Air Lakitan Watershed

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

^{3}/s. From this research, it can be concluded that the Log-Pearson Type III distribution is the frequency distribution that matches the hydrological analysis in the research area. This method can be applied in analyses of river levels in other areas with heavy rainfall. Therefore, the water level upstream and downstream is the same at 0.41 m with a discharge of 1 m

^{3}/s; the river cross-section downstream with an existing discharge of 0.024 m

^{3}/s produces water height as high as 0.08 m and with a flow rate of 0.783 m/s, the water level at the downstream cross-section is filled up to 0.75 m high, and the water level downstream of the irrigation channel is up to 0.40 m.

## 1. Introduction

## 2. Methods

#### 2.1. Data and Investigation

- Location (administrative, coordinates, river name, and others).
- Determination of the measurement location boundary and topographic reference point.
- Water sources and irrigation water availability.
- Condition of irrigation networks (maps and schemes).
- Irrigation management status.
- Water supply, distribution, and water supply plans, cropping plans, drying plans, etc.
- Estimated area of the service area to be irrigated.
- Estimated benefits derived from plans for building a water divider building (tapping building).
- Institutional irrigation Operation and Maintenance (OM).

#### 2.2. Research Location

## 3. Hydrograph Stream Flow Analysis

_{i}is rainfall data; C

_{s}is the skewness coefficient; X

_{r}= mean value; C

_{k}is the coefficient of kurtosis; and n is the amount of data.

- (1)
- Dispersion of logarithms is normally distributed (two parameters). Characteristics: the constants C
_{s}= 3 C_{v}and C_{s}are always positive; mathematical formula for a probability line: x(t) = x + K; x(t) = rainfall depth, with t being the return period (years); K = frequency factor. - (2)
- Probability is spread out evenly in a normal fashion. Characteristics: expected value of C
_{s}= 0; P(x − S) = 15.87%; P(x) = 50.00%; P(x + S) = 84.14%. Variables with values between −S and +S have a 68.27% chance of occurring, while values between −X and +X have a 95.44% chance. - (3)
- Dispersion of Gumbel type I. Characteristics: C
_{s}= 1.3960 cv; C_{k}= 5.4002; mathematical formula for a probability line:$$X\left(t\right)=x+\frac{\sigma}{{\sigma}_{n}}\left(y-{y}_{n}\right)$$_{n}is the mean value and σ_{n}is reduced variated of standard deviation; y is reduced variated and σ is standard deviation. - (4)
- Log-Pearson Type III distribution. There is no evidence that the statistical data follows any of the three aforementioned distributions. The accumulated precipitation is converted to its natural logarithm, with x
_{i}values replaced by ln x_{i}. Once this is done, it can be computed for the mean, standard deviation, and skewness coefficient:$$\mathrm{ln}x=\frac{{{\displaystyle \sum}}_{i=1}^{n}ln{x}_{i}}{n}$$$$s=\sqrt{\frac{{{\displaystyle \sum}}_{i=1}^{n}{\left(ln{x}_{i}-lnx\right)}^{2}}{\left(n-1\right)}}$$$${C}_{s}=\frac{n}{\left(n-1\right)\left(n-2\right){S}^{3}}{{\displaystyle \sum}}_{i=1}^{n}{\left(ln{x}_{i}-lnx\right)}^{3}$$

_{s}computed in Equation (9). Testing the goodness of fit with Smirnov–Kolmogorov and chi-square tests was carried out to see whether the available data fall under the selected theoretical distribution.

- Determination of the length of the rain data series (for example, n years).
- Data for each year are broken down from large to small.
- For each year, the data are taken (k + 1) the largest data, where k is the number of events equaled or exceeded in the desired year. n years are obtained from n × (k + 1) data.
- The new data set is sorted from large to small.
- Rainfall with probability equaled or exceeded k times a year is data in order (n × k + 10).

## 4. Results and Discussion

#### 4.1. Statistical Data Analysis

_{v}), coefficient of skewness (C

_{s}), and kurtosis coefficient (C

_{k}) were obtained as follows:

_{v}) = 0.368.

_{s})= 1.9245.

_{k}) = 9831.

#### 4.2. Time of Concentration (t_{c})

_{c}), several formulas are used, namely Kraven, Rhiza, and Kirpich [10].

#### 4.2.1. Kraven Formula

_{c}= L/W

_{c}: time of concentration (s)

#### 4.2.2. Rhiza Formula

_{c}= L/W

_{c}= time of flood concentration (h)

#### 4.2.3. Kirpich Formula

_{c}= m 0.00013 L

^{0.77}S

^{−}

^{0.383}

_{c}= time of flood concentration (h)

_{c}) = 0.824 min was obtained.

#### 4.3. Rainfall Intensity

#### 4.3.1. Ishiguro

#### 4.3.2. Mononobe

_{c}(time of concentration). The two formulas (Formulas (15) and (16)) above are suitable for an area of irrigation of >100 Km

^{2}.

#### 4.4. Hydrodynamic Modeling Analysis

#### 4.5. HEC-RAS Program

#### Cross Section Data

- The coordinates (
**Station, Elevation**) of the latitude points on the River Sta are as follows: (0, 3), (2, 1), (4, 1), (6, 3). Remember, the base slope of the channel is 0.001 so the elevation at River Sta “1000” is 1 m above the elevation at River Sta “0” [18]. - Fill in the distance of the River Sta section “1000” to the downstream reach lengths with the number “1000” (the unit of length is meters), both for LOB, Channel, and ROB [19].
- Fill in Manning’s n Values, Main Channel Bank Stations, and Cont\Exp Coefficients do not need to be changed [20].

#### 4.6. Data Input

^{3}/s producing water height as high as 0.08 m.

^{3}/s producing water height as high as 0.41 m.

^{3}/s producing water height as high as 0.404 m.

## 5. Conclusions

- The Log-Pearson Type III distribution is the frequency distribution that matches the hydrological analysis in the research area. This method can be applied in analyses of river levels in other areas with heavy rainfall.
- The water level upstream and downstream is the same at 0.41 m with a discharge of 1 m
^{3}/s. - The river cross-section downstream with the existing discharge of 0.024 m
^{3}/s produces water height as high as 0.08 m. - With a flow rate of 0.783 m/s, the water level at the downstream cross-section is filled up to 0.75 m high, and the water level downstream of the irrigation channel is up to 0.40 m.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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Years | Rainfall (X) | LOG X | (X − X_{average})^{2} | (X − X_{average})^{3} | (X − X_{average})^{4} |
---|---|---|---|---|---|

1989 | 346 | 2.539 | 0.009 | −0.000805 | 0.000075 |

1990 | 448 | 2.651 | 0.000 | 0.000007 | 0.000000 |

1991 | 518 | 2.714 | 0.007 | 0.000556 | 0.000046 |

1993 | 441 | 2.644 | 0.000 | 0.000002 | 0.000000 |

1994 | 468 | 2.670 | 0.001 | 0.000055 | 0.000002 |

1995 | 417 | 2.620 | 0.000 | −0.000002 | 0.000000 |

1996 | 231 | 2.364 | 0.072 | −0.019358 | 0.005198 |

1997 | 298 | 2.474 | 0.025 | −0.003937 | 0.000622 |

1998 | 558 | 2.747 | 0.013 | 0.001502 | 0.000172 |

1999 | 365 | 2.562 | 0.005 | −0.000340 | 0.000024 |

2000 | 347 | 2.540 | 0.008 | −0.000773 | 0.000071 |

2001 | 626 | 2.797 | 0.027 | 0.004448 | 0.000731 |

2014 | 545 | 2.736 | 0.011 | 0.001134 | 0.000118 |

2015 | 417 | 2.620 | 0.000 | −0.000002 | 0.000000 |

2016 | 634 | 2.802 | 0.029 | 0.004910 | 0.007059 |

Amount of data | 15 | ||||

Amount | 39.482 | 0.113 | 0.0144 | 0.014118 | |

Average | 2.632 | C_{s} | |||

Standard of deviation | 0.090 | Ck |

Distribution Type | Terms | Calculation | Conclusion |
---|---|---|---|

Normal | C_{s} ≈ 0 | C_{s} = 1.9245 | No, fulfill |

C_{k} ≈ 3 | C_{k} = 9.831 | ||

Gumbel | C_{s} = 1.1396 | C_{s} = 1.9245 | No, fulfill |

C_{k} = 5.4002 | C_{k} = 9.831 | ||

Log Normal | C_{s} (ln x) = 0 | C_{s} (ln x) = −0.2133 | No, fulfill |

C_{k} (ln x) = 3 | C_{k} (ln x) = 3.4689 | ||

Log-Pearson Type III | Apart from top value | C_{s} = −0.2133 | Fulfill |

C_{k} = 3.4689 |

T | P(%) | C_{s} | G | Log X | X (mm) |
---|---|---|---|---|---|

2 | 50 | 0.2133 | −0.0373 | 2.0576 | 114 |

5 | 20 | 0.2133 | 0.8376 | 2.1894 | 155 |

10 | 10 | 0.2133 | 1.3117 | 2.2608 | 182 |

20 | 5 | 0.2133 | 1.7461 | 2.3262 | 212 |

25 | 4 | 0.2133 | 1.8329 | 2.3393 | 218 |

50 | 2 | 0.2133 | 2.1723 | 2.3904 | 246 |

Tr (Year) | R_{24} (mm) | I (mm/h) |
---|---|---|

5 | 114 | 45,0343 |

10 | 155 | 60,9973 |

25 | 182 | 71,8987 |

50 | 212 | 83,5867 |

100 | 218 | 86,1431 |

_{24}is rain for 24 h or 1 day.

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**MDPI and ACS Style**

Syarifudin, A.; Satyanaga, A.; Destania, H.R.
Application of the HEC-RAS Program in the Simulation of the Streamflow Hydrograph for Air Lakitan Watershed. *Water* **2022**, *14*, 4094.
https://doi.org/10.3390/w14244094

**AMA Style**

Syarifudin A, Satyanaga A, Destania HR.
Application of the HEC-RAS Program in the Simulation of the Streamflow Hydrograph for Air Lakitan Watershed. *Water*. 2022; 14(24):4094.
https://doi.org/10.3390/w14244094

**Chicago/Turabian Style**

Syarifudin, Achmad, Alfrendo Satyanaga, and Henggar Risa Destania.
2022. "Application of the HEC-RAS Program in the Simulation of the Streamflow Hydrograph for Air Lakitan Watershed" *Water* 14, no. 24: 4094.
https://doi.org/10.3390/w14244094