# Development of Rainfall Intensity, Duration and Frequency Relationship on a Daily and Sub-Daily Basis (Case Study: Yalamlam Area, Saudi Arabia)

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Study Area

^{2}. The basin boundary, situated in the downstream area, is extended to include virtually all of the lower flat area. From the high altitudes of the Hijaz Mountains, near Taif, Wadi Yalamlam starts from the Al Shafa region. This has an annual average rainfall of 140 mm. The wadi has various altitudes, ranging widely from 2600 to 25 m. A general location map and a digital elevation model (DEM) of Wadi Yalamlam are shown in Figure 1. The higher and lower parts of the basin are dominated by incisive natural vegetation. Quaternary deposits and sand dunes, on the other hand, followed by tiny dispersed fragments, greatly alter the granitoid and metamorphosed basaltic slopes, the constituents of the lower part of the wadi [28].

## 3. Methodology and Data Collection

_{t}is estimated precipitation depth (mm) for the duration of t hours, P

_{24}is depth of daily precipitation (mm) and t is duration (h).

- -
- Method A

- -
- Method B

_{T}(in mm) for each duration with a set return time T (in year) for the Gamble distribution.

_{T}= P

_{ave}+ KS

_{ave}is the average of the maximum precipitation corresponding to a specific duration.

_{i}is the individual extreme value of rainfall and n is the number of events or years of record. The standard deviation is calculated by Equation (5) computed using the following relation:

_{d}is durations in hours.

_{T}, P*

_{ave}and S* are as defined previously but based on the logarithmically transformed P

_{i}values, i.e., P* of Equation (7). K

_{T}is the Pearson frequency factor which depends on return period (T) and skewness coefficient (C

_{s}).

_{s}, is required to compute the frequency factor for this distribution. The skewness coefficient was computed by Equation (11) [31,32].

_{T}values can be determined from tables [31]. The frequency factor K

_{T}for the Log-Pearson type III distribution may be extracted by knowing the coefficient of skewness and the recurrence period. The solution antilog in Equation (8) provides the projected extreme value for the return time.

- -
- IDF formula development

^{b}, c denotes the straight line’s slope.

- -
- Determine the natural logarithm for the (K) value obtained from the Gumbel distribution or the Log-Pearson type III distribution, as well as the natural logarithm for the rainfall period T.
- -
- Draw the log (I) values on the y axis and the log(T) values on the x axis for each return periods.
- -
- Using the graphs, we obtained the value of c for all recurrence intervals, and then we used the following equation to find the average (c
_{ave}) value, by using the following equation:

## 4. Results and Discussion

_{T}for any design storm with a specified duration t

_{d}(min) and return time T

_{r}(years) for the Yalamlam area, you can use Equation (15) or Figure 9.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 6.**IDF curves by Log-Pearson type III distribution of Yalamlam area (Methods A, B and observed).

**Figure 7.**Comparison of IDF curves between two methods and observed with return periods 100 and 25 years using Gumbel distribution.

**Figure 8.**Comparison of IDF curves between two methods and observed with return periods 100 and 25 years using Log-Pearson type III distribution.

Basin Area (A) | 1665 (km^{2}) |

Basin Slope (BS) | 0.1308 (m/m) |

Average Overland Flow (AOFD) | 1.23 (km) |

Basin lengths (L) | 88.01 (km) |

Mean Basin elevation (AVEL) | 771.84 (m) |

Max Flow Distance (MFD) | 110.8 (km) |

Max Flow Slope (MFS) | 0.0210 (m/m) |

Centroid stream Distance (CSD) | 68.8 (km) |

Station | J-204 |
---|---|

Sample size | 30 |

Minimum (mm) | 12.6 |

Maximum (mm) | 110 |

Median (mm) | 41.6 |

Mean (mm) | 44.5 |

Standard deviation | 23.3 |

Variation coefficient | 0.524 |

Skewness coefficient | 1.14 |

Kurtosis coefficient | 3.54 |

Stations | Gumbel | GEV | Gamma | Normal | LPT III | |||||
---|---|---|---|---|---|---|---|---|---|---|

Chi-Square | K-S | Chi-Square | K-S | Chi-Square | K-S | Chi-Square | K-S | Chi-Square | K-S | |

J-204 | 2 | 0.113 | 3.2 | 0.112 | 4.8 | 0.118 | 4.8 | 0.119 | 3.2 | 0.11 |

Return Period (Year) | 2 | 5 | 10 | 25 | 50 | 100 |

Gumbel (mm) | 40.4 | 60.1 | 73.2 | 89.6 | 102 | 114 |

Log-Pearson type III | 39.7 | 60.5 | 74.8 | 93.3 | 107 | 121 |

Duration (min) | Rainfall Intensity (mm/h) | |||||
---|---|---|---|---|---|---|

Return Period of 100-Year | Return Period of 25-Year | |||||

Method (A) | Method (B) | Observed | Method (A) | Method (B) | Observed | |

10 | 224.7 | 282 | 181.2 | 178.2 | 221.4 | 142.2 |

30 | 128.6 | 114.8 | 111 | 101 | 90 | 86.4 |

60 | 78 | 64.3 | 69.8 | 61.3 | 50.5 | 54.8 |

120 | 45.3 | 36.7 | 37.6 | 35.6 | 28.9 | 29.9 |

360 | 19.9 | 14.9 | 15.5 | 15.5 | 11.7 | 12.3 |

1440 | 4.8 | 4.8 | 4.8 | 3.8 | 3.8 | 3.8 |

**Table 6.**The rainfall intensity of 100- and 25-year return periods using Log-Pearson type III distribution.

Duration (min) | Rainfall Intensity (mm/h) | |||||
---|---|---|---|---|---|---|

Return Period of 100-Year | Return Period of 25-Year | |||||

Method (A) | Method (B) | Observed | Method (A) | Method (B) | Observed | |

10 | 254.4 | 304.8 | 122.4 | 187.2 | 232.2 | 115.2 |

30 | 138.8 | 124 | 79.2 | 105.8 | 94.4 | 73 |

60 | 84.3 | 69.4 | 56.9 | 64.2 | 52.9 | 49.4 |

120 | 49 | 39.9 | 33.9 | 37.3 | 30.2 | 28.3 |

360 | 21.4 | 16.1 | 16.8 | 16.3 | 12.3 | 12.9 |

1440 | 5.2 | 5.2 | 5.2 | 3.9 | 3.9 | 3.9 |

Duration (h) | 24 h Rainfall (%) |
---|---|

24 | 1.00 |

12 | 0.87 |

8 | 0.80 |

6 | 0.76 |

4 | 0.70 |

3 | 0.66 |

2 | 0.61 |

1 | 0.53 |

0.5 (30 min) | 0.46 |

0.25 (15 min) | 0.40 |

0.167 (10 min) | 0.37 |

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**MDPI and ACS Style**

Kawara, A.Q.; Elsebaie, I.H.
Development of Rainfall Intensity, Duration and Frequency Relationship on a Daily and Sub-Daily Basis (Case Study: Yalamlam Area, Saudi Arabia). *Water* **2022**, *14*, 897.
https://doi.org/10.3390/w14060897

**AMA Style**

Kawara AQ, Elsebaie IH.
Development of Rainfall Intensity, Duration and Frequency Relationship on a Daily and Sub-Daily Basis (Case Study: Yalamlam Area, Saudi Arabia). *Water*. 2022; 14(6):897.
https://doi.org/10.3390/w14060897

**Chicago/Turabian Style**

Kawara, Atef Q., and Ibrahim H. Elsebaie.
2022. "Development of Rainfall Intensity, Duration and Frequency Relationship on a Daily and Sub-Daily Basis (Case Study: Yalamlam Area, Saudi Arabia)" *Water* 14, no. 6: 897.
https://doi.org/10.3390/w14060897