# Relationship of Rainfall and Flood Return Periods through Hydrologic and Hydraulic Modeling

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area and Data

^{2}with a length of about 260 km. The wet period is from November to February with the rainiest months being November to December. On the other hand, during the summer months (June to August), the rainfall is almost zero. The mean annual flow for the Pineios River basin is estimated at about 3500 × 10

^{6}m

^{3}. According to Bathrellos et al. [39], the regime of the Pineios River flow, for the main tributary, can be characterized as perennial, with large differences between winter and summer. For instance, near its delta, the mean average discharge ranges from more than 150 m

^{3}/s in February and March to about 10 m

^{3}/s in August and September [39].

^{2}[38]. The altitude ranges from 67 m a.s.l. to about 2700 m a.s.l. with the mean altitude estimated at about 421 m a.s.l. Figure 2 also presents the land uses in the study area, according to 2018 Corine Land Cover. These data were used for estimating different parameters (e.g., CN parameter) needed for the hydrologic simulation. The land use/land cover types are presented in detail in Table 1, i.e., Corine code, description and percent of the total study area covered per land use/land cover type.

- Satellite rainfall is free of biases;
- The rainfall distribution is produced based on the empirical Alternating Block Method [1] assuming specific time step and storm duration;
- The rainfall losses are estimated using the SCS Curve Number (CN, land uses and soil in the study area);
- Continuous simulation and flood flow frequency analysis was conducted using the peak discharges generated by the hydrological model;
- One flood per hydrological year is selected so that the events are identically distributed and statistically independent.

#### 2.2. Extreme Value Analysis

^{2}). Point rainfall depth was transformed to areal rainfall depth by multiplying it with the aforementioned coefficient.

#### 2.3. Hydrologic-Hydrodynamic Modeling

_{c}) and the constant rate of the Deficit and Constant loss method, in a manual and empirical way. The parameters used and their range are presented in Table 3. Finally, flood frequency analysis was applied to the annual maxima series, which resulted from the continuous simulation, using Gumbel and GEV theoretical distributions, in order to estimate flood quantiles for various return periods (2 years to 100 years) as previously described.

## 3. Results

#### 3.1. Design Storm Approach vs. Flood Frequency Analysis

^{3}/s.

^{3}/s to 156.1 m

^{3}/s. The maximum flow was estimated at about 5101 m

^{3}/s, while the minimum flow was 959.2 m

^{3}/s. The runoff coefficient was calculated equal to 0.36.

#### 3.2. Hydrodynamic Simulations and Results

^{2}larger flooded area. Similarly, greater inundation depths emerged from the flood frequency analysis approach, resulting in discrepancies of up to 1 m between the examined scenarios (Figure 8b) for the areas close to the downstream boundary of the model.

## 4. Discussion

## 5. Summary and Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Distribution function plot for Annual Maxima Series (AMS) of various time scales and GEV fitted distributions (LM—Linear Moments).

**Figure 4.**Event based simulation results for rainfall duration of 48 h and return period of 50 years.

**Figure 6.**Distribution function plot for Annual Maxima Series (AMS) and Gumbel and GEV fitted distributions (LM—Linear Moments).

**Figure 7.**Comparison of the two approaches (design storm and continuous simulation and flood frequency analysis) in terms of (

**a**) return period and peak discharges, and (

**b**) relationship of rainfall return period to flood return period.

**Figure 8.**Difference between design storm approach and continuous simulation and flood frequency analysis approach with respect to the (

**a**) flood extents and (

**b**) inundation depths downstream of the catchment.

**Figure 9.**Flow velocity (m/s) distribution for the (

**a**) design storm approach and (

**b**) continuous simulation and flood frequency analysis approach downstream of the catchment.

Corine Code | Description | Percent of Total Area (%) | Corine Code | Description | Percent of Total Area (%) |
---|---|---|---|---|---|

111 | Continuous urban fabric | 0.03 | 243 | Land principally occupied by agriculture, with significant areas of natural vegetation | 5.52 |

112 | Discontinuous urban fabric | 2.12 | 311 | Broad-leaved forest | 9.13 |

121 | Industrial or commercial units | 0.20 | 312 | Coniferous forest | 3.87 |

122 | Road and rail networks and associated land | 0.07 | 313 | Mixed forest | 2.30 |

131 | Mineral extraction sites | 0.06 | 321 | Natural grasslands | 7.87 |

133 | Construction sites | 0.08 | 322 | Moors and heathland | 0.28 |

141 | Green urban areas | 0.02 | 323 | Sclerophyllous vegetation | 11.84 |

142 | Sport and leisure facilities | 0.07 | 324 | Transitional woodland-shrub | 7.84 |

211 | Non-irrigated arable land | 13.48 | 331 | Beaches, dunes, sands | 0.09 |

212 | Permanently irrigated land | 30.45 | 332 | Bare rocks | 0.02 |

221 | Vineyards | 0.18 | 333 | Sparsely vegetated areas | 0.66 |

222 | Fruit trees and berry plantations | 0.02 | 334 | Burnt areas | 0.03 |

223 | Olive groves | 0.16 | 411 | Inland marshes | 0.09 |

231 | Pastures | 1.46 | 511 | Water courses | 0.47 |

242 | Complex cultivation patterns | 1.47 | 512 | Water bodies | 0.11 |

TOTAL | - | 100 |

Time Scale | ||||||||
---|---|---|---|---|---|---|---|---|

Statistical Parameter | 30 min | 1 h | 2 h | 3 h | 6 h | 12 h | 24 h | 48 h |

Sample size | 21 | 21 | 21 | 21 | 21 | 21 | 21 | 21 |

Maximum | 37.00 | 40.00 | 72.00 | 75.00 | 105.60 | 117.35 | 139.55 | 149.65 |

Minimum | 6.90 | 12.75 | 20.00 | 29.25 | 29.55 | 34.55 | 37.70 | 46.05 |

Mean | 15.06 | 23.44 | 36.80 | 44.83 | 57.35 | 66.43 | 74.77 | 83.47 |

Geometric mean | 13.85 | 22.15 | 34.69 | 43.01 | 55.12 | 63.78 | 71.19 | 79.88 |

Median | 15.00 | 21.26 | 34.85 | 43.00 | 50.30 | 59.81 | 66.55 | 76.80 |

Standard deviation | 6.90 | 8.09 | 13.48 | 13.75 | 17.34 | 20.18 | 25.30 | 26.89 |

Coefficient of skewness | 1.76 | 0.54 | 1.06 | 0.88 | 1.18 | 1.02 | 1.16 | 1.18 |

Coefficient of kurtosis | 4.33 | −0.65 | 1.08 | −0.28 | 1.64 | 0.83 | 0.98 | 0.76 |

Coefficient of variation (CoV) | 0.46 | 0.35 | 0.37 | 0.31 | 0.30 | 0.30 | 0.34 | 0.32 |

Q1 | 10.35 | 15.90 | 27.05 | 35.10 | 46.35 | 54.10 | 60.00 | 66.70 |

Q3 | 16.30 | 28.04 | 42.53 | 53.18 | 64.71 | 77.50 | 77.50 | 86.70 |

IQR | 5.95 | 12.14 | 15.48 | 18.08 | 18.36 | 23.40 | 17.50 | 20.00 |

Quartile Skew | −0.56 | 0.12 | −0.01 | 0.13 | 0.57 | 0.51 | 0.25 | −0.01 |

Parameters (Units) | Range | Adjusted Value |
---|---|---|

Maximum deficit (mm)-L | 35–120 | 78 |

Constant rate (mm/h)-L | 2–8 | 2 |

Initial deficit (mm)-L | 15–60 | 39 |

Impervious (%)-L | 0–100 | 2 |

Crop coefficient (k_{c})-C | 0.1–0.5 | 0.19 |

Initial storage (%)-C | 0–50 | 50 |

Maximum storage (mm)-C | 2–7 | 4.5 |

**Table 4.**Intensity (mm/h) for various rainfall durations (2 to 48 h) and for return periods ranging from 2 to 100 years.

Intensity (mm/h) for Return Period (Years) | ||||||
---|---|---|---|---|---|---|

Duration (h) | 2 | 5 | 10 | 25 | 50 | 100 |

2 | 18.07 | 22.54 | 26.36 | 32.06 | 36.92 | 42.31 |

3 | 14.20 | 17.72 | 20.72 | 25.20 | 29.02 | 33.26 |

6 | 8.89 | 11.09 | 12.97 | 15.78 | 18.17 | 20.82 |

12 | 5.30 | 6.61 | 7.73 | 9.40 | 10.83 | 12.41 |

24 | 3.07 | 3.83 | 4.47 | 5.44 | 6.27 | 7.18 |

48 | 1.75 | 2.18 | 2.55 | 3.10 | 3.57 | 4.09 |

Statistics | |||
---|---|---|---|

Sample size | 22 | Coefficient of skewness | 0.64 |

Maximum | 5101.40 | Coefficient of kurtosis | 0.33 |

Minimum | 959.20 | Coefficient of variation (CoV) | 0.39 |

Mean | 2736.36 | Q1 | 2121.93 |

Geometric mean | 2533.70 | Q3 | 3042.55 |

Median | 2640.25 | IQR | 920.63 |

Standard deviation | 1064.43 | Quartile Skew | −0.13 |

Return Period (Years) | Design Storm Approach (m^{3}/s) | Flood Frequency Analysis (m^{3}/s) | Percent Increase (%) | ||
---|---|---|---|---|---|

Gumbel | GEV | Gumbel | GEV | ||

2 | 909.8 | 2556.5 | 2589.2 | 181 | 185 |

5 | 1516.4 | 3523.9 | 3554.1 | 132 | 134 |

10 | 2102.0 | 4164.5 | 4162.1 | 98 | 98 |

25 | 3062.3 | 4973.8 | 4896.7 | 62 | 60 |

50 | 3946.5 | 5574.2 | 5418.5 | 41 | 37 |

100 | 4972.9 | 6170.1 | 5917.7 | 24 | 19 |

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**MDPI and ACS Style**

Vangelis, H.; Zotou, I.; Kourtis, I.M.; Bellos, V.; Tsihrintzis, V.A. Relationship of Rainfall and Flood Return Periods through Hydrologic and Hydraulic Modeling. *Water* **2022**, *14*, 3618.
https://doi.org/10.3390/w14223618

**AMA Style**

Vangelis H, Zotou I, Kourtis IM, Bellos V, Tsihrintzis VA. Relationship of Rainfall and Flood Return Periods through Hydrologic and Hydraulic Modeling. *Water*. 2022; 14(22):3618.
https://doi.org/10.3390/w14223618

**Chicago/Turabian Style**

Vangelis, Harris, Ioanna Zotou, Ioannis M. Kourtis, Vasilis Bellos, and Vassilios A. Tsihrintzis. 2022. "Relationship of Rainfall and Flood Return Periods through Hydrologic and Hydraulic Modeling" *Water* 14, no. 22: 3618.
https://doi.org/10.3390/w14223618