# A Chronology-Based Wave Input Reduction Technique for Simulations of Long-Term Coastal Morphological Changes: An Application to the Beach of Mastichari, Kos Island, Greece

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Physiographic Setting

#### 2.2. Bathymetry and Topography

^{®},v.10.8).

#### 2.3. Wind and Wave Climate

#### 2.4. Wave Input Reduction Techniques

#### 2.4.1. The Energy Flux Method

^{3}), g is the gravity acceleration (9.81 m

^{2}/s), ${H}_{m0}$ is the significant wave height of the wave record, and $Cg$ is the group wave celerity in deep water, which is estimated as $\mathrm{g}{T}_{p}/4\pi $, depending on the ${T}_{p}$ of the wave record.

#### 2.4.2. A Wind and Wave Chronology-Based Input Reduction Technique

#### 2.4.3. A Wave Chronology-Based Input Reduction Technique

#### 2.4.4. Simulations

- A simulation consisting of the full time series at the offshore boundary, which is denoted as the reference/benchmark simulation.
- Five repetitive simulations using the 12 representatives in random order, which were calculated by the energy flux input reduction method and are denoted as the energy flux simulation with five repetitions. The average of 5 repetitions is in accordance with [4], the authors of which used the same approach for estimating the average performance score of the Energy Flux Method. In this study, the average result of the 5 repetitions was estimated as the expected result, considering the uncertainty of the random order of the 12 representative scenarios and its effect on the final result.
- A simulation consisting of a time series of representatives of wind-wave events and swell events, which have been extracted by the wave input reduction technique of Malliouri et al. [22], which is denoted hereafter as the wind and wave chronology- based input reduction technique.
- A set of three simulations consisting of isolated sequences of the representative scenarios of wave events with similar characteristics based on the three criteria (see Equation (8)) for specific $\mathsf{\Delta}h$, $\mathsf{\Delta}t$, and $\mathsf{\Delta}d$ values and specific morphological acceleration factors (MORFAC), which are denoted hereafter as the wave chronology- based input reduction techniques.

#### 2.5. Numerical Model Setup

#### 2.6. Evaluation of Wave Input Reduction Techniques

## 3. Results

#### 3.1. Representative Wave Conditions

#### 3.2. Numerical Models Results

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The study area of the coast of Mastichari and the offshore wind and wave data extraction point in Kos island, Greece.

**Figure 2.**The three mesh density level zones in the computational domain, and the baseline, the coastline, the edge line, and the active profile elements used in the Shoreline Morphology module. Created in MIKE 21 mesh generator environment.

**Figure 4.**Rose diagram of wind velocity ${U}_{w}$ (

**left**) and significant wave height ${H}_{m0}$ (

**right**) in the year 2021.

**Figure 5.**The 12 equal Energy Flux bins (rectangles) and the 12 representative wave conditions (red circles) derived from the Energy Flux Method (1 January 2021–31 December 2021).

**Figure 6.**The extraction of wave events time series from an indicative subset of data by the wind and wave chronology-based reduction technique (

**up**) and the wave chronology-based reduction techniques (

**below**) using different values for $\mathsf{\Delta}h$, $\mathsf{\Delta}t$, and $\mathsf{\Delta}d$.

**Figure 7.**Diagrams of the reference time series and the four chronology-based reduction techniques’ time series for ${H}_{m0}$ (

**up**), ${T}_{p}$ (

**middle**), and $MWD$ (

**below**).

**Figure 8.**Scatter diagrams of the coefficients of variation towards the mean values of ${H}_{m0}$ and ${T}_{p}$ of the produced wave events using the four chronology-based reduction techniques.

**Figure 9.**Visual comparison of the reference simulation and the applied wave input reduction techniques simulations regarding the final bottom evolution at the end of 2021.

**Figure 10.**Bottom-level evolution maps at specific time steps of the year 2021 obtained by the wave chronology-based input reduction technique (5th simulation).

s/n | Reduction Technique | ΜORFAC | $\mathit{d}\mathit{t}\text{}\left(\mathbf{s}\right)$ |
---|---|---|---|

1 | Reference simulation | 1 | 3600 |

2 | Energy Flux (5 rep.) | 15 | 3600 |

3 | Wind and wave chronology | 5 | 1800 |

4 | Wave chronology: $\mathsf{\Delta}h$ = 0.2 m, $\mathsf{\Delta}t$ = 0.5 s, $\mathsf{\Delta}d$ = 10 deg. | 5 | 1800 |

5 | Wave chronology: $\mathsf{\Delta}h$ = 0.5 m, $\mathsf{\Delta}t$ = 1.0 s, $\mathsf{\Delta}d$ = 15 deg. | 10 | 1800 |

6 | Wave chronology: $\mathsf{\Delta}h$ = 0.8 m, $\mathsf{\Delta}t$ = 1.5 s, $\mathsf{\Delta}d$ = 20 deg. | 15 | 1800 |

s/n | Reduction Technique | Μorfac | dt (s) | Model Run-Time (hr) | Run-Time Reduction | $\mathit{B}\mathit{S}\mathit{S}$ |
---|---|---|---|---|---|---|

1 | Referrence simulation | 1 | 3600 | 14.65 | - | - |

2 | Energy Flux (5 rep.) | 15 | 3600 | 4.82 | 67% | 0.70 |

3 | Wind and wave chronology | 5 | 1800 | 6.71 | 54% | 0.87 |

4 | Wave chronology: $\mathsf{\Delta}h$ = 0.2 m, $\mathsf{\Delta}t$ = 0.5 s, $\mathsf{\Delta}d$ = 10 deg. | 5 | 1800 | 8.42 | 43% | 0.96 |

5 | Wave chronology: $\mathsf{\Delta}h$ = 0.5 m, $\mathsf{\Delta}t$ = 1.0 s, $\mathsf{\Delta}d$ = 15 deg. | 10 | 1800 | 4.07 | 72% | 0.85 |

6 | Wave chronology: $\mathsf{\Delta}h$ = 0.8 m, $\mathsf{\Delta}t$ = 1.5 s, $\mathsf{\Delta}d$ = 20 deg. | 15 | 1800 | 3.23 | 78% | 0.69 |

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**MDPI and ACS Style**

Malliouri, D.I.; Petrakis, S.; Vandarakis, D.; Moraitis, V.; Goulas, T.; Hatiris, G.-A.; Drakopoulou, P.; Kapsimalis, V.
A Chronology-Based Wave Input Reduction Technique for Simulations of Long-Term Coastal Morphological Changes: An Application to the Beach of Mastichari, Kos Island, Greece. *Water* **2023**, *15*, 389.
https://doi.org/10.3390/w15030389

**AMA Style**

Malliouri DI, Petrakis S, Vandarakis D, Moraitis V, Goulas T, Hatiris G-A, Drakopoulou P, Kapsimalis V.
A Chronology-Based Wave Input Reduction Technique for Simulations of Long-Term Coastal Morphological Changes: An Application to the Beach of Mastichari, Kos Island, Greece. *Water*. 2023; 15(3):389.
https://doi.org/10.3390/w15030389

**Chicago/Turabian Style**

Malliouri, Dimitra I., Stelios Petrakis, Dimitrios Vandarakis, Vyron Moraitis, Tatiana Goulas, Georgios-Angelos Hatiris, Paraskevi Drakopoulou, and Vasilios Kapsimalis.
2023. "A Chronology-Based Wave Input Reduction Technique for Simulations of Long-Term Coastal Morphological Changes: An Application to the Beach of Mastichari, Kos Island, Greece" *Water* 15, no. 3: 389.
https://doi.org/10.3390/w15030389