# Modelling of Deep Learning-Based Downscaling for Wave Forecasting in Coastal Area

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

#### 2.1. Downscaling

#### 2.2. Wave Model SWAN

#### 2.3. Long Short-Term Memory

_{t}, i

_{t}, and o

_{t}, as shown in Figure 3. Gate f

_{t}is the forget gate, i

_{t}is the input gate, and o

_{t}is the output gate. The first step in assembling the LSTM is to differentiate the necessary and unnecessary data. A sigmoid function defines this process. This step is followed by saving and updating the data in cells from new inputs. There are two procedures in this step: the sigmoid function, which decides whether new information should be updated or discarded in the numerical value forms 0 and 1, and the tanh function, which assigns a value to each passed data, determines the value of the data in the numbers −1 to 1 [22]. The equations for each gate are given by Equations (4)–(7).

_{fx}, W

_{fs}, W

_{ix}, W

_{is}, W

_{cx}, W

_{cs}, ${W}_{\mathit{ox}}$, ${W}_{\mathit{os}}$ is the weight; ${b}_{\mathit{f}}$, ${b}_{\mathit{i}}$, ${b}_{\mathit{c}}$, ${b}_{\mathit{o}}$ is the bias; ${X}_{\mathit{t}}$ is the input; ${S}_{t-1}$ is the previous state; ${c}_{t}$ is the cell state or memory cell; and $\sigma $ is the activation function sigmoid. The forget gate determines the information stored or discarded in the previous state. The input gate regulates how many states the current input passes through. The output gate decides the internal state to forward and the cell state or memory cell to forward old information with additional new information to the next cell state.

#### 2.4. Bidirectional Long Short-Term Memory

## 3. Methodology

#### 3.1. Wave Data Generation

#### 3.1.1. Data Generation for Jakarta Bay Case

#### 3.1.2. Data Generation for Meulaboh Case

#### 3.2. Deep Learning Approach for Wave Downscaling

## 4. Results and Discussion

#### 4.1. Wave Downscaling in Jakarta Bay

#### 4.2. Wave Downscaling in Meulaboh

#### 4.2.1. Sensitivity of Length of Training Data

#### 4.2.2. Sensitivity of Length of Downscaling

#### 4.2.3. Comparison with Wave Observation

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Sample Availability

## References

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**Figure 1.**Snapshot of significant wave height from global forecast model GFS, with grid size of 0.25${}^{\xb0}$.

**Figure 5.**Flowchart of wave data generation. The wave dataset is obtained by performing continuous wave simulation using phase-averaged wave model SWAN.

**Figure 6.**Snapshot of significant wave height on 6 December 2020, at 06:00 UTC, from SWAN simulation in domain I.

**Figure 8.**Snapshot of significant wave height on 1 March 2020, at 00:00 UTC, from wave simulation using SWAN model for domains II (

**left plot**) and III (

**right plot**) for Meulaboh area.

**Figure 9.**Flowchart of machine learning optimisation. The wave dataset from the previous step is used as training data for machine learning.

**Figure 11.**The spatial correlation map at Jakarta Bay was obtained by calculating the correlation coefficient (CC) between Hs at the global grid and Hs at the targeted local domain. Big dots denote CC values: upper left plot for CC values ≥ 0.70, upper right plot for ≥0.80, and lower plot for ≥0.90.

**Figure 12.**Comparison of significant wave height from wave observation with result of prediction by using BiLSTM at Jakarta Bay.

**Figure 14.**Spatial correlation maps at Meulaboh offshore, obtained by calculating the correlation coefficient (CC) between Hs at the global grid with Hs at a targeted local domain. Big dots denote CC values: in the upper plot for CC values ≥ 0.70, the lower plot for CC values ≥ 0.80, and the lower plot for CC values ≥ 0.90.

**Figure 15.**Comparison of significant wave height from wave observation with result of prediction by using BiLSTM at offshore of Meulaboh.

Domain | Lon (${}^{\xb0}$) | Lat (${}^{\xb0}$) | $\Delta $x | $\Delta $y | $\mathit{N}\mathit{x}$ | $\mathit{N}\mathit{y}$ | ||
---|---|---|---|---|---|---|---|---|

West | East | South | North | |||||

1 | 0.5 | 175.5 | −69.5 | 30.5 | 1.4957 | 1.4925 | 117 | 67 |

2 | 100 | 132 | −15 | 5 | 0.25 | 0.25 | 128 | 80 |

3 | 106.65 | 107.05 | −6.122 | −5.858 | 0.0027 | 0.0027 | 150 | 99 |

Domain | Lon (${}^{\xb0}$) | Lat (${}^{\xb0}$) | $\Delta $x | $\Delta $y | $\mathit{N}\mathit{x}$ | $\mathit{N}\mathit{y}$ | ||
---|---|---|---|---|---|---|---|---|

West | East | South | North | |||||

1 | 0.5 | 175.5 | −69.5 | 30.5 | 1.4957 | 1.4925 | 117 | 67 |

2 | 85 | 107 | −14 | 14 | 0.25 | 0.25 | 88 | 112 |

3 | 96 | 96.25 | 4 | 4.15 | 0.002 | 0.002 | 125 | 75 |

**Table 3.**Comparison between selected spatial correlation with results of downscaling performance for prediction 14 days ahead in Jakarta Bay area.

Area | Selected Spatial Correlation | Number of Wave Point Input | CC | RMSE |
---|---|---|---|---|

Jakarta Bay | CC > 0.70 | 32 | 0.84 | 0.07 |

CC > 0.80 | 23 | 0.85 | 0.08 | |

CC > 0.90 | 6 | 0.87 | 0.07 |

**Table 4.**Comparison between the significant wave height Hs from wave observation at Jakarta Bay with the results of GFS Forecast, downscaling using LSTM and BiLSTM.

Model | RMSE |
---|---|

LSTM | 0.15 |

BiLSTM | 0.14 |

GFS Forecast | 0.19 |

**Table 5.**Comparison between selected spatial correlation with results of downscaling performance for prediction 14 days ahead in Meulaboh area.

Area | Selected Spatial Correlation | Number of Wave Point Input | CC | RMSE |
---|---|---|---|---|

Meulaboh | CC > 0.70 | 52 | 0.95 | 0.16 |

CC > 0.80 | 50 | 0.96 | 0.16 | |

CC > 0.90 | 4 | 0.97 | 0.15 |

**Table 6.**Sensitivity of the training data length with the accuracy of the prediction using LSTM and BiLSTM.

Length (Year) | LSTM | BILSTM | ||||
---|---|---|---|---|---|---|

CC | RMSE | MAPE | CC | RMSE | MAPE | |

1 | 0.91 | 0.22 | 15.06 | 0.93 | 0.21 | 14.53 |

5 | 0.95 | 0.17 | 13.77 | 0.95 | 0.19 | 13.70 |

10 | 0.96 | 0.18 | 12.9 | 0.96 | 0.17 | 12.11 |

15 | 0.97 | 0.17 | 12.41 | 0.97 | 0.16 | 11.79 |

20 | 0.96 | 0.18 | 12.23 | 0.97 | 0.17 | 12.46 |

25 | 0.96 | 0.18 | 12.13 | 0.97 | 0.17 | 11.44 |

30 | 0.96 | 0.16 | 11.29 | 0.97 | 0.16 | 10.65 |

40 | 0.97 | 0.17 | 11.8 | 0.97 | 0.15 | 11.40 |

**Table 7.**Sensitivity of the downscaling prediction length with the resulting accuracy of downscaling.

Downscaling Length (Day) | CC | RMSE | MAPE |
---|---|---|---|

1 | 0.99 | 0.01 | 0.72 |

3 | 0.99 | 0.06 | 8.46 |

5 | 0.99 | 0.09 | 13.42 |

7 | 0.99 | 0.08 | 10.47 |

14 | 0.97 | 0.16 | 11.79 |

**Table 8.**Comparison between the significant wave height Hs from wave observation at Meulaboh with GFS forecast results, downscaling using LSTM and BiLSTM.

Model | RMSE |
---|---|

LSTM | 0.19 |

BiLSTM | 0.16 |

GFS Forecast | 0.23 |

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**MDPI and ACS Style**

Adytia, D.; Saepudin, D.; Tarwidi, D.; Pudjaprasetya, S.R.; Husrin, S.; Sopaheluwakan, A.; Prasetya, G. Modelling of Deep Learning-Based Downscaling for Wave Forecasting in Coastal Area. *Water* **2023**, *15*, 204.
https://doi.org/10.3390/w15010204

**AMA Style**

Adytia D, Saepudin D, Tarwidi D, Pudjaprasetya SR, Husrin S, Sopaheluwakan A, Prasetya G. Modelling of Deep Learning-Based Downscaling for Wave Forecasting in Coastal Area. *Water*. 2023; 15(1):204.
https://doi.org/10.3390/w15010204

**Chicago/Turabian Style**

Adytia, Didit, Deni Saepudin, Dede Tarwidi, Sri Redjeki Pudjaprasetya, Semeidi Husrin, Ardhasena Sopaheluwakan, and Gegar Prasetya. 2023. "Modelling of Deep Learning-Based Downscaling for Wave Forecasting in Coastal Area" *Water* 15, no. 1: 204.
https://doi.org/10.3390/w15010204