# Ensemble Neural Networks for the Development of Storm Surge Flood Modeling: A Comprehensive Review

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## Abstract

**:**

## 1. Introduction

## 2. Neural Network Ensemble

## 3. Theoretical Framework

#### 3.1. Neural Network Architectures

#### 3.2. Transfer Learning

#### 3.3. Ensemble Generation Methods

## 4. Ensemble Pruning and Fine-Tuning

## 5. Data Preparation

#### 5.1. Raw Input Data

**Table 4.**Description and main features of the most widely used storm and flood datasets. The symbol ✓indicates that the feature is included, while the symbol ✗signifies that the feature is not included.

Dataset | Description | Features | Source |
---|---|---|---|

North Atlantic Coast Comprehensive Study (NACCS) | A combined set of 1050 synthetic tropical and 100 synthetic extratropical storms using the coupled ADCIRC/STWAVE models | ✓ Consistent across the entire North Atlantic Coast region. | The U.S. Army Corps of Engineers (USACE) [146] |

✓ Covers storm surge, sea level rise, and erosion | |||

✓ Easily accessible | |||

✗ Coarse spatial resolution | |||

✗ Limited temporal scope | |||

✗ Relies on certain assumptions and uncertainties | |||

ECMWF Re-Analysis (ERA5) | The latest generation of atmospheric reanalysis of the global climate with detailed information on a wide range of atmospheric variables. | ✓ High temporal and spatial resolution | Copernicus Climate Change Service (C3S), the joint C3S-NOAA project [147,148] |

✓ Covers a wide range of atmospheric variables | |||

✓ Publicly available | |||

✗ Complex and may require advanced technical skills | |||

✗ Limited vertical resolution (137 pressure levels) | |||

Global Extreme Sea-Level Analysis Version 2 (GESLA-2) | Provides 39148 years of sea level data from 1355 station records, with information on extreme sea levels, including storm surges, tidal cycles, and rise in sea level. | ✓ Covers a wide range of extreme sea-level events | University of Hawaii and the National Oceanic and Atmospheric Administration (NOAA) [2] |

✓ Consistent across the entire globe and different geographic locations | |||

✓ Publicly available | |||

✗ Gaps in the data particularly for remote or sparsely populated regions. | |||

✗ Relies on certain assumptions and uncertainties | |||

✗ Limited information on coastal morphology and human activities | |||

NOAA Global Real Time Ocean Forecasting System (RTOFS global | provides nowcasts (analyses of near-present conditions) and forecast guidance on up to eight days of ocean temperature and salinity, water velocity, sea surface elevation, sea ice coverage, and sea ice thickness. | ✓ Provides high-quality and updated oceanographic and meteorological data in real time | National Centers for Environmental Prediction (NCEP), NOAA [4] |

✓ Global coverage | |||

✓ High spatial and temporal resolution | |||

✓ Integration with other models for a more comprehensive understanding of storm surge | |||

✗ Limited data availability for a particular area or time period | |||

✗ Relies on certain assumptions and uncertainties | |||

✗ Requires significant computational resources | |||

Coastal Hazards System (CHS) | National coastal storm hazard data resource for probabilistic coastal hazard assessment (PCHA) results and statistics, including measurements of water level, wind speed, and wave height | ✓ High-quality data | Pacific Coastal and Marine Science Center of the United States Geological Survey (USGS) [149] |

✓ High spatial resolution with detailed information about storm surge patterns | |||

✓ Provides historical data | |||

✗ Limited to the coastal areas of the United States | |||

✗ Limited temporal resolution for predicting a storm surge during an ongoing event | |||

✗ Needs to be integrated with other models to make accurate predictions | |||

The Sea, Lake and Overland Surges from Hurricanes (SLOSH) model | Uses a combination of historical storm data, topographical data, and numerical algorithms to simulate the impact of a hurricane on coastal areas and predict storm surge heights and flooding potential associated with hurricanes. | ✓ Specifically designed and tested for storm surge prediction | National Oceanic and Atmospheric Administration (NOAA) [150] |

✓ Can be customized to specific geographic areas | |||

✓ Can be integrated with other models, such as atmospheric and wave models | |||

✗ Resource-intensive | |||

✗ Limited data availability (requires input data, such as atmospheric pressure and wind speed) | |||

✗ Limited spatial resolution | |||

✗ Relies on certain assumptions and uncertainties | |||

National Water Level Observation Network (NWLON) | A network of tide gauges that can be used for storm surge prediction. | ✓ Specifically designed and tested for storm surge prediction | National Oceanic and Atmospheric Administration’s (NOAA) Center for Operational Oceanographic Products and Services (CO-OPS) [151] |

✓ Provides historical data | |||

✓ Wide geographic coverage throughout the United States | |||

✗ Limited spatial resolution | |||

✗ Lack of a comprehensive model for predicting storm surge (needs to be integrated with other models) | |||

✗ Limited data availability in all coastal regions |

#### 5.2. Data Preprocessing and Wrangling

## 6. Model Selection and Evaluation

#### 6.1. Bias–Variance Tradeoff

#### 6.2. Ensemble Diversity

#### 6.3. Probabilistic Performance

## 7. Summary

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A. Implementation of Backward Propagation of Errors

- Defining the sigmoid activation function and its derivative

1 def activation(x):

2 return 1 / (1 + np.exp(-x))

3 def activation_derivative(x):

4 return activation(x) * (1 - activation(x))

- Defining the forward propagation function

1 def forward_propagation(x, weights, biases):

`2 a = [x]`

`3 z = []`

4 for l in range(1, len(weights) + 1):

`5 z.append(np.dot(weights[l], a[l-1]) + biases[l])`

`6 a.append(activation(z[l-1]))`

7 return a, z

- Defining the backward propagation function

1 def backward_propagation(x, y, a, z, weights, biases, learning_rate):

`2 L = len(weights)`

`3 delta = [None] * (L + 1)`

`4 gradients = {}`

- Running the error propagation using the chain rule $\frac{\partial L}{\partial w}=\frac{\partial L}{\partial h}\frac{\partial h}{\partial z}\frac{\partial z}{\partial w}$, $h={f}_{\left(z\right)}$, and Loss Function $L=\frac{1}{n}\sum _{j=1}^{n}({h}_{j}-{y}_{j})$

1 # Compute the output layer delta

`2 delta[L] = (a[L] - y) * activation_derivative(z[L-1])`

3 # Compute deltas (*@\color{codegreen}\textbf{for}@*) the hidden layers

4 for l in range(L-1, 0, -1):

`5 delta[l] = np.dot(weights[l+1].T, delta[l+1]) * activation_derivative(z[l-1])`

6 # Compute gradients (*@\color{codegreen}\textbf{for}@*) weights and biases

7 for l in range(1, L+1):

`8 gradients[f’dW{l}’] = np.dot(delta[l], a[l-1].T)`

`9 gradients[f’db{l}’] = delta[l]`

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**Figure 1.**(

**a**) Best track positions and storm surge predictions from the empirical CHRPS model compared to water level observations from select NOAA tide gauge and storm surge predictions from operational ADCIRC simulations performed at CHL [39]. (

**b**) Winds. (

**c**) Hourly heights. (

**d**) Barometric pressure. (

**e**) Air temperature. (

**f**) Sea surface temperature in Aransas Wildlife Refuge station, TX, for Hurricane Harvey (August 2017).

**Figure 2.**Flow diagram of transfer learning in NN, including the reuse of a pre-trained model on a new problem.

**Figure 3.**Flow diagram of transfer learning in NN involving the reuse of a pre-trained model on a new problem.

**Figure 10.**Qualitative assessment of studies numbered 1 to 6 from Table 2.

Activation Function | Equation | Python Library | Applications |
---|---|---|---|

ReLU (Rectified Linear Unit) | $f\left(x\right)=max(0,x)$ | tensorflow, keras | MLP, CNN |

Sigmoid | $f\left(x\right)=\frac{1}{1+{e}^{-x}}$ | tensorflow, keras | RNN |

Tanh (Hyperbolic Tangent) | $f\left(x\right)=\frac{{e}^{x}-{e}^{-x}}{{e}^{x}+{e}^{-x}}$ | tensorflow, keras | RNN |

Softmax | $f\left({x}_{j}\right)=\frac{{e}^{{x}_{j}}}{{\sum}_{k=1}^{K}{e}^{{x}_{k}}}$ | tensorflow, keras | Classification, normalizing the output |

Leaky ReLU | $f\left(x\right)=max(\alpha x,x)$ | tensorflow, keras | MLP, CNN |

Physical Components | Training/Optimization Procedures | Regularization |
---|---|---|

Number of hidden layers within the network | Defining the optimizer algorithm | Degree of regularization (lambda) |

Number of hidden Neurons | Configuring the learning rate | Number of active neurons (dropout rate) |

Choice of key activation function | Defining the main type of loss function | |

Choice of evaluation metric for regression problem | ||

Number of training samples (mini-batch) | ||

Setting the random initialization | ||

Number of training cycles (epochs) |

**Table 3.**Comparative analysis of ensemble approaches, evaluation metrics, and data collection in different studies (2015–2022).

Study Number | Target Goal | Methodology | Ensemble Approach | Evaluation Metric | Data Collection |
---|---|---|---|---|---|

1 [42] | Low-probability peak storm surge height due to TCs | ANN and coupled ADCIRC + SWAN simulations | GBDTR and AdaBoost Regressor | RAE, MRAE, and RMSE | Synthetic TCs + Historical typhoon data in the New York metropolitan area |

2 [115] | Storm tide and resurgence | Hydrodynamic and Hydrologic Ensemble Forecast | Stacking (super-ensemble) based on RMSE and bias correction | RMSE, PRE, and COU | US mid-Atlantic and Northeast coastline wind and tide data |

3 [43] | Hourly surge time series at the global scale | ANN, CNN, LSTM, and ConvLSTM | Bootstrap aggregation | RMSE and CRPS | GESLA Version 2 tide station database |

4 [37] | Peak storm surges from TC track time series | C1PKNet (1D CNN, principal component analysis, and k-means clustering) | Average of ten trained C1PKNet model predictions | MSE and CC | NACCS synthetic TC surge database |

5 [83] | Real time and accurate storm surge | CNN and LSTM, transfer learning | – | RMSE, MAE, and CC | Storm surge level time series in the southeastern coastal region of China |

6 [116] | Rapid prediction of storm surge time series | ANN and CSTORM-MS coupled model | – | RMSE and CC | Synthetic storms in the Gulf of Mexico |

**Table 5.**General comparison between the datasets in Table 4. The symbol ✓indicates that the feature is included, while the symbol ✗ signifies that the feature is not included.

NACCS | ERA5 | GESLA2 | RTOFS | CHS | SLOSH | NWLON | |
---|---|---|---|---|---|---|---|

Spatial resolution | 0.25 degrees | 0.25 degrees | 0.25 degrees | 0.08 to 0.25 degrees | 0.02 to 0.05 degrees | 0.02 to 0.05 degrees | 0.08 to 0.33 degrees |

Temporal resolution | 6 h | Hourly | Monthly | Hourly | Hourly | Hourly | Hourly |

Coverage | North Atlantic Coast region | Global | Global | Global | Coastal areas of the United States | Atlantic and Gulf coasts of the United States | Coastal areas of the United States |

Availability | Open access | Open access (needs license for real-time products) | Open access | Open access | Limited access | Limited access | Open access |

Complexity | Highly complex | Highly complex | Complex | Complex | Fairly complex | Complex | Fairly complex |

Possible data gap | Incomplete coverage or missing data for certain time periods | Missing or incomplete weather station data in certain regions or periods | Limited or no data on certain sea levels and time periods | Incomplete coverage or missing data for certain time periods | Incomplete coverage or missing data for certain time periods | Missing or incomplete data for certain hurricanes or regions | Incomplete coverage or missing data for certain time periods |

Integration with other models | ✓ | ✗ | ✓ | ✓ | ✓ | ✓ | ✓ |

SID | ISO_TIME | NATURE | LAT | LON | WMO_WIND | WMO_PRES | DIST2LAND | LANDFALL |
---|---|---|---|---|---|---|---|---|

degrees_N | degrees_E | kts | mb | km | km | |||

2017228N14314 | 8/25/2017 3:00 | TS | 25.2924 | −94.7578 | 243 | 204 | ||

2017228N14314 | 8/25/2017 6:00 | TS | 25.6 | −95.1 | 90 | 966 | 204 | 170 |

2017228N14314 | 8/25/2017 9:00 | TS | 25.935 | −95.4651 | 160 | 133 | ||

2017228N14314 | 8/25/2017 12:00 | TS | 26.3 | −95.8 | 95 | 949 | 133 | 123 |

2017228N14314 | 8/25/2017 15:00 | TS | 26.6999 | −96.0652 | 126 | 108 | ||

2017228N14314 | 8/25/2017 18:00 | TS | 27.1 | −96.3 | 105 | 943 | 108 | 67 |

2017228N14314 | 8/25/2017 21:00 | TS | 27.4875 | −96.5806 | 67 | 34 | ||

2017228N14314 | 8/26/2017 0:00 | TS | 27.8 | −96.8 | 115 | 941 | 34 | 11 |

2017228N14314 | 8/26/2017 3:00 | TS | 28 | −96.9 | 115 | 937 | 11 | 0 |

2017228N14314 | 8/26/2017 6:00 | TS | 28.2 | −97.1 | 105 | 948 | 0 | 0 |

2017228N14314 | 8/26/2017 9:00 | TS | 28.4534 | −97.2205 | 0 | 0 |

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**MDPI and ACS Style**

Nezhad, S.K.; Barooni, M.; Velioglu Sogut, D.; Weaver, R.J.
Ensemble Neural Networks for the Development of Storm Surge Flood Modeling: A Comprehensive Review. *J. Mar. Sci. Eng.* **2023**, *11*, 2154.
https://doi.org/10.3390/jmse11112154

**AMA Style**

Nezhad SK, Barooni M, Velioglu Sogut D, Weaver RJ.
Ensemble Neural Networks for the Development of Storm Surge Flood Modeling: A Comprehensive Review. *Journal of Marine Science and Engineering*. 2023; 11(11):2154.
https://doi.org/10.3390/jmse11112154

**Chicago/Turabian Style**

Nezhad, Saeid Khaksari, Mohammad Barooni, Deniz Velioglu Sogut, and Robert J. Weaver.
2023. "Ensemble Neural Networks for the Development of Storm Surge Flood Modeling: A Comprehensive Review" *Journal of Marine Science and Engineering* 11, no. 11: 2154.
https://doi.org/10.3390/jmse11112154