# Optimizing the Performance of Coupled 1D/2D Hydrodynamic Models for Early Warning of Flash Floods

^{1}

^{2}

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## Abstract

**:**

^{2}. We perform calculations for 8 scenarios that combined various grid sizes (with approximately 44,000–95,000 control volumes) with the use of the SWE or DWE. We derive the following conclusions: (i) calculated maximum water depths using DWE were equal to 60–65% of the corresponding water depths using SWE, i.e., the DWE significantly underestimated water depths; (ii) calculated total inundation areas using the SWE were approximately 4.9–7.9% larger than the corresponding inundation areas using the DWE; these differences can be considered as acceptable; and (iii) the total computation times using SWE, which ranged from 67 to 127 min, were 60–70% longer than the computation times using DWE.

## 1. Introduction

- T1: Threshold-based flood alert service that is based on real-time data measurements of river flow and/or water elevation along streams and rivers.
- T2: Flood forecasting service that involves simple simulation tools and models, such as statistical curves, level-to-level correlations or time-of-travel relationships that may allow a quantified and time-based prediction of water elevation to provide a flood warning to an acceptable degree of confidence and reliability.
- T3: Vigilance mapping internet service that produces a map-based visualization of flood-risk levels, derived from observations or models, which are characterized by a color code indicating the severity of the expected flood.
- T4: Flood inundation forecasting service that predicts flood-risk via the use of integrated hydrologic-hydrodynamic models with sufficient accuracy of the extent of the potentially flooded areas, such as housing areas and critical infrastructure locations, including power stations and road or rail bridges [7].

## 2. Materials and Methods

#### 2.1. The Area of Study

^{2}and 22.0 km

^{2}, respectively. In 2017, these streams that pass through the town of Mandra were characterized by significant reductions in their available cross-sectional areas and the occurrence of floods even at low flow rates due to the intensive construction activities in the greater area; these characteristics were one of the main reasons for the disaster that occurred in November 2017 [13]. Immediately after this catastrophic event, flood protection works in Mandra were constructed according to their Final Study performed in 2014 for a design flood having a return period equal to 50 years. The flood protection works include mainly (1) the regulation of Soures St for a length of 1780 m (x = 239–1695 m) for a design flow equal to 91 m

^{3}/s and 125 m

^{3}/s (x = 0–239 m), and (2) the diversion of Agia Aikaterini St to Soures St via a 1451 m long channel for a design flow equal to 47 m

^{3}/s.

#### 2.2. The HEC-RAS 1D/2D Hydrodynamic Model

^{2}),

^{3}/T),

^{2}/T),

_{s}= water surface elevation (L),

^{2}), and

_{f}= friction slope (-).

^{2}),

_{t,xx}and v

_{t,yy}= horizontal eddy viscosity in the x and y directions, respectively (L

^{2}/T),

_{b,x}and τ

_{b,y}= bottom shear stresses on the x and y directions, respectively (M/L/T

^{2}),

^{3}), and

_{t}= eddy viscosity tensor (L

^{2}/T) and

_{L}= user-defined mixing coefficient in the longitudinal direction (-)

_{T}= user-defined mixing coefficient in the transverse direction (-)

_{s}= Smagorinsky coefficient that ranges from 0.05 to 0.2

_{s}= 0.05 and D

_{L}= 0.3 and D

_{T}= 0.1 are adopted.

#### 2.3. The Computational Domain and Grid

^{2}that includes the total flood inundation areas that is around 3.0 km

^{2}[20]. In this domain, the 1D and the 2D numerical grids were constructed using a digital surface model (DSM) of a very high resolution equal to 0.80 m × 0.80 m to capture all hydraulically important features of the area’s surface, including streets, trees, and buildings, that are required for detailed hydrodynamic calculations and were “corrected” via an accurate topographic survey performed during the construction of the flood protection works.

- A1: Along Agia Aikaterini St.
- A2: Along the main streets of the residential area of the town of Mandra.
- B1: Along the main streets of the residential area of the town of Magoula.
- B2: Along the industrial park of the town of Mandra.
- NR: Along the National Road Eleusina-Thebes (NRET).
- NO: Along the National Road Olympia (NRO).
- AR: Along the Attica Road.
- LS: Along the Louka Street.

#### 2.4. Scenarios of Calculations

## 3. Results and Discussion

#### 3.1. Calculated Maximum Water Depths and Velocities

- Calculated water depths for the scenarios DWE-1, DWE-2, and DWE-3 do not show significant differences from the DWE-4; the calculated RMSE was around 9%. Thus, practically, a relatively coarse grid DWE-1 can be used for the calculations using DWE.
- Calculated water depths for the scenarios SWE-1, SWE-2, and SWE-3 show greater differences from the SWE-4 than the corresponding DWE scenarios; the calculated RMSE ranges from 9% to 16%. Thus, calculations with SWE require much finer grids that should be determined after performing grid independence calculations for the specific case under examination.
- Calculated maximum water depths using DWE are equal to 60% to 65% of the corresponding values using SWE, i.e., the DWE significantly underestimated water depths.

#### 3.2. Calculated Inundation Areas

- Calculated total inundation areas for the scenarios DWE-1, DWE-2, and DWE-3 show small differences (less than 3.1%) from the DWE-4.
- Calculated total inundation areas for the scenarios SWE-1, SWE-2, and SWE-3 that use SWE also show small differences (less than 5.2%) from the SWE-4, which however, are higher than the corresponding DWE scenarios.
- Calculated total inundation areas using the SWE are larger than those calculated using the DWE by approximately 4.9–7.9%; the higher values were observed for the finer grids.

#### 3.3. Calculated Flood Arrival Times

- For the DWE scenarios, the flood arrives faster than in the SWE scenarios due to the generally lower water velocities and higher water depths predicted by the SEW scenarios. The delays of the SWE scenarios range from 0 to 4 min in Agia Aikaterini St and from 3 to 8 min for Soures St.
- Calculated flood arrival times generally show an independence of the grid size for the scenarios with the two finer grids, except these of the very coarse grids, DWE-1 and SWE-1, that show significant differences from the finest grids that range from −9 min (earlier arrival) to +5 min (later arrival-delay) for the SWE and up to 13 min (delay) for the DWE.

#### 3.4. Computational Times

#### 3.5. Discussion

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**The area of study with the main streams and the flood protection works; the numbered small triangles denoted as L1 to L9 indicate the monitoring locations where flood arrival times are calculated.

**Figure 7.**Comparison of hydrographs for the water depth and flow rate in the cross-section that passes through the monitoring location L5.

**Figure 9.**Comparison of total computational time to number of control volumes for scenarios DWE-4 and SWE-4.

Scenario | Dimensions of Main Mesh (m × m) | Dimensions of Mesh in A2, B1, and NR (m × m) | Dimensions of Mesh in A1, B2, NO, AR, and LS (m × m) | Number of Control Volumes Area A | Number of Control Volumes Area B | Number of Control Volumes Area C | Total Number of Control Volumes | Computational Time (min) |
---|---|---|---|---|---|---|---|---|

DWE-1 | 50 × 50 | 5 × 5 | 10 × 10 | 18,423 | 19,564 | 5982 | 43,969 | 42.05 |

DWE-2 | 40 × 40 | 5 × 5 | 10 × 10 | 19,630 | 20,358 | 7617 | 47,605 | 44.97 |

DWE-3 | 20 × 20 | 5 × 5 | 10 × 10 | 30,778 | 26,314 | 21,859 | 78,951 | 67.40 |

DWE-4 | 20 × 20 | 2 × 2 | 10 × 10 | 46,890 | 26,314 | 21,859 | 95,063 | 74.47 |

SWE-1 | 50 × 50 | 5 × 5 | 10 × 10 | 18,423 | 19,564 | 5982 | 43,969 | 66.87 |

SWE-2 | 40 × 40 | 5 × 5 | 10 × 10 | 19,630 | 20,358 | 7617 | 47,605 | 77.83 |

SWE-3 | 20 × 20 | 5 × 5 | 10 × 10 | 30,778 | 26,314 | 21,859 | 78,951 | 107.33 |

SWE-4 | 20 × 20 | 2 × 2 | 10 × 10 | 46,890 | 26,314 | 21,859 | 95,063 | 126.72 |

**Table 2.**Extent of the total inundation area (km

^{2}) and differences between various scenarios (%).

Scenario | Inundation Area | Difference between Corresponding Scenarios (DWE-SWE/SWE) | Difference from Scenario DWE-4 | Difference from Scenario SWE-4 |
---|---|---|---|---|

DWE-1 | 2.63 | −5.9% | −3.1 | - |

DWE-2 | 2.64 | −3.0% | −2.8 | - |

DWE-3 | 2.72 | −7.6% | 0.2 | - |

DWE-4 | 2.72 | −7.9% | 0.0 | - |

SWE-1 | 2.80 | 5.9% | - | −5.2 |

SWE-2 | 2.72 | 3.0% | - | −4.5 |

SWE-3 | 2.95 | 7.6% | - | −0.1 |

SWE-4 | 2.95 | 7.9% | - | 0.0 |

SCENARIO | L1 | L2 | L3 | L4 | L5 | L6 | L7 | L8 | L9 |
---|---|---|---|---|---|---|---|---|---|

Agia Aikaterini St | Soures St | ||||||||

DWE-1 | 5:22 | 5:40 | 5:52 | 6:05 | 6:02 | 6:14 | 7:23 | 7:06 | 7:40 |

DWE-2 | 5:22 | 5:42 | 5:51 | 6:04 | 6:00 | 6:13 | 7:19 | 6:57 | 7:35 |

DWE-3 | 5:22 | 5:40 | 5:52 | 6:01 | 6:02 | 6:14 | 7:15 | 6:55 | 7:28 |

DWE-4 | 5:22 | 5:40 | 5:50 | 6:01 | 6:02 | 6:14 | 7:15 | 6:55 | 7:27 |

SWE-1 | 5:10 | 5:34 | 5:44 | 6:00 | 6:01 | 6:16 | 7:21 | 7:02 | 7:40 |

SWE-2 | 5:22 | 5:41 | 5:48 | 6:02 | 6:06 | 6:19 | 7:20 | 7:03 | 7:33 |

SWE-3 | 5:22 | 5:40 | 5:52 | 6:05 | 6:10 | 6:22 | 7:18 | 7:02 | 7:35 |

SWE-4 | 5:22 | 5:40 | 5:52 | 6:05 | 6:10 | 6:22 | 7:18 | 7:02 | 7:35 |

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**MDPI and ACS Style**

Mitsopoulos, G.; Panagiotatou, E.; Sant, V.; Baltas, E.; Diakakis, M.; Lekkas, E.; Stamou, A.
Optimizing the Performance of Coupled 1D/2D Hydrodynamic Models for Early Warning of Flash Floods. *Water* **2022**, *14*, 2356.
https://doi.org/10.3390/w14152356

**AMA Style**

Mitsopoulos G, Panagiotatou E, Sant V, Baltas E, Diakakis M, Lekkas E, Stamou A.
Optimizing the Performance of Coupled 1D/2D Hydrodynamic Models for Early Warning of Flash Floods. *Water*. 2022; 14(15):2356.
https://doi.org/10.3390/w14152356

**Chicago/Turabian Style**

Mitsopoulos, Georgios, Elpida Panagiotatou, Vasiliki Sant, Evangelos Baltas, Michalis Diakakis, Efthymios Lekkas, and Anastasios Stamou.
2022. "Optimizing the Performance of Coupled 1D/2D Hydrodynamic Models for Early Warning of Flash Floods" *Water* 14, no. 15: 2356.
https://doi.org/10.3390/w14152356