# A Review of Application of Machine Learning in Storm Surge Problems

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## Abstract

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## 1. Introduction

## 2. The Formulation of Prediction Problems

#### 2.1. Water Level Forecasting

#### 2.1.1. Peak-Value Forecasting

- Predict peak water levels in a single station.

- Predict peak water levels in several stations.

#### 2.1.2. Time-Series Forecasting

- Direct strategy

- Recursive strategy

- Joint strategy

#### 2.1.3. Spatio-Temporal Forecasting

- Predict peak water levels.

- Predict the temporal evolution of water levels.

#### 2.2. Inundation Forecasting

#### 2.2.1. Peak-Value Forecasting

#### 2.2.2. Time-Series Forecasting

#### 2.2.3. Spatio-Temporal Forecasting

#### 2.3. Importance of Formulating Problems

## 3. Data Collection and Feature Selection

#### 3.1. Observational Data

#### 3.1.1. Typhoon Characteristics

#### 3.1.2. Local Hydrodynamic Parameters

#### 3.1.3. Local/Regional Meteorological Conditions

#### 3.2. Synthetic Data

Study | Area | Number of Synthetic Typhoons | Numerical Models | Methods Used to Generate Storms | Inclusion of Astronomical Tide |
---|---|---|---|---|---|

Jia and Taflanidis [37] | the Hawaiian Islands of Oahu and Kauai | 643 | ADCIRC+SWAN | Based on guidance from the Central Pacific Hurricane Center | √ |

Kim et al. [67]; Jia et al. [86] | Gulf of Mexico | 446 | ADCIRC+ STWAVE | Defined from a joint probability model | × |

Al Kajbaf and Bensi [19]; Hashemi et al. [20]; Lee et al. [52]; Adeli et al. [54]; Kyprioti et al. [55]; Wei et al. [87]; | North Atlantic, Rhode Island | 1050 (Some studies only used part of synthetic typhoons) | A suite of numerical models including: WAM, STWAVE, ADCIRC | JPM-OS (Joint probability method with optimized sampling methodology) | × |

Bezuglov et al. [88] | North Carolina | 324 | ADCIRC+WW3+SWAN | JPM | × |

Sahoo and Bhaskaran [42] | the entire Odisha State, India | 44 | ADCIRC | Cyclone tracks obtained from the archives of JTWC | √ |

Igarashi and Tajima [64] | Tokyo Bay | 151 | Storm surge models based on nonlinear shallow-water equations and energy balance equations | Historical typhoons from 1951 to 2017 | × |

Ayyad et al. [89] | the Western North Atlantic Ocean | 10,300 | ADCIRC+SWAN | Statistical/deterministic TC model based on observations or climate models | Not mentioned |

Ayyad et al. [90] | the Western North Atlantic Ocean basin (idealized topography) | 36,892 | ADCIRC | Statistical/deterministic TC model based on observations | Not mentioned |

Lockwood et al. [91] | The entire North Atlantic Ocean | 5018 | ADCIRC | Based on the NCEP reanalysis between 1980 and 2005 | × |

Xie et al. [48] | the Pearl River and adjacent East China Sea | 116 | FVCOM | Historical typhoons from 1958–2018 | √ |

Pachev et al. [57] | Texas and Alaska | Texas: 446, Alaska: 109 | ADCIRC | JPM-OS | √For Alaska ×For Texas |

#### 3.3. Feature Engineering, Feature Selection and Feature Importance

#### 3.3.1. Feature Engineering

- Scaling, such as scaling distance between reference and targeted locations measured by maximum wind radius, is one simple way to add features [19].
- Lagged features are frequently used to capture temporal dependencies and patterns, which represent values at preceding timesteps, providing information about the future state. It has been confirmed that the appropriate historical horizons (a.k.a. sliding window widths and lags) have a direct impact on the model performance [38,45,53,62,64].
- Temporal/Spatial window statistics, like mean, max, and min over a fixed window, are considered for specific tasks. For example, to remove the temporal component of the input data, Pachev et al. [57] computed the rolling window statistics of the atmospheric features for predicting peak surges. To account for the spatial dependency of forcing variables or bathymetry, spatial features were added by computing statistics for each targeted point over a sequence of neighborhoods [53,57,92].
- Time-series decomposition technique. Wang et al. [47] showed that the fluctuation features of the storm surge extracted by the time-varying filtered empirical modal and the use of Fourier transform can significantly improve forecasting performance.

#### 3.3.2. Feature Selection

#### 3.3.3. Feature Importance

## 4. The Selection of Proper ML Methods

#### 4.1. Conventional Machine Learning Models

#### 4.1.1. Gaussian Process Regression

#### 4.1.2. Support Vector Regression

#### 4.1.3. Genetic Algorithms and Genetic Programming

#### 4.1.4. Artificial Neural Networks

#### 4.1.5. Nonlinear Autoregressive Exogenous Model

#### 4.1.6. Other Models

#### 4.2. Deep Learning Models

#### 4.2.1. LSTM

#### 4.2.2. CNN

#### 4.2.3. CNN-LSTM, LSTM-CNN, and ConvLSTM

#### 4.3. Model Selection, Development and Evaluation

- Choose a well-established, commonly-used model or a familiar model used in previous tasks (e.g., ANNs, CNNs, and LSTMs) to get started.
- In terms of types of problem forvmulation, if probabilistic outcomes are required, Gaussian Process Regression and Polynomial Chaos are preferred, and other schemes that are unused before could be experimented with (e.g., Bayesian framework [27]). If classification problems are to be handled, some simple and frequently used algorithms, such as KNN, SVM, and DT, can be tried at first. Storm surge forecasting is often referred to as a regression task, and a bunch of regression models can be employed.
- In terms of available data, conventional ML models are more qualified in small-size datasets, while if a large synthetic dataset is accessible, the performance of DL models will be greatly enhanced.
- In terms of the tradeoff between accuracy and interpretability, using which algorithm depends on the objective of the problem. In general, as the complexity of a method increases, its interpretability decreases. If the goal is higher accuracy, it’s better to prioritize models with more complex internal structures (e.g., DNNs and encoder-decoder models) without pursuing excessive interpretation. If a functional form is needed and features are only a few, a white-box model like GP can be used.

^{2}) [81,125], and correlation coefficient (CC) [45,48]. In particular, the Kling-Gupta Efficiency (KGE) [53] accounts for three different important aspects of the reconstructed time series, including correlation coefficient variability and bias ratio term, thus providing comprehensive insights into how well the storm surge time series are reproduced. For probabilistic predictions, the Continuous Ranked Probability Score (CRPS) [92] is a widely used metric that averages the difference between the observed and predicted cumulative distribution of the surge across all lead times and for deterministic forecasting, it reduces to the MAE. For storm surge problems, a good forecasting model is qualified for both capturing the entire spatio-temporal evolution of water levels and minimizing the errors of peak values. Further useful guidance for researchers interested in systematically maximizing the performance of deep learning can be found in the Deep Learning Tuning Playbook by Godbole et al. [133].

## 5. Application of Hybrid Methods in Storm Surge Prediction

#### 5.1. ML-Based Post-Processing

#### 5.2. ML-Aided Optimization of Numerical Model Parameterization

#### 5.3. ML-Based Data Assimilation

## 6. Discussion

#### 6.1. Underprediction of Peak Values and Extreme Events

#### 6.2. The Nonlinear Interaction Problems

#### 6.3. The Black-Box Problems

#### 6.4. When Does ML Perform Better than Traditional Methods?

## 7. Summary and Future Outlooks

#### 7.1. Physics-Informed ML

#### 7.1.1. PIML in Storm Surge Modelling

#### 7.1.2. PIML-Aided Numerical Forecasting

#### 7.2. Towards a Transparent and Robust AI-Aided Storm Surge Warning System

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

AdaBoost | Adaptive Boost |

ADCIRC | ADvanced CIRCulation model |

AI | Artificial Intelligence |

ALE | Accumulated Local Effects |

ANFIS | Adaptive Neuro-Fuzzy Inference System |

ANN | Artificial Neural Network |

BPNN | Back-Propagation Neural Network |

CC | Correlation Coefficient |

ChatGPT | Chat Generative Pre-Trained Transformer |

CMA | China Meteorological Administration |

CNN | Convolutional Neural Network |

ConvLSTM | Convolutional LSTM |

CRPS | Continuous Ranked Probability Score |

DL | Deep Learning |

DNN | Deep Neural Network |

DT | Decision Trees |

EnKf | Ensemble Kalman Filter |

ENSO | El Niño/La Niña Southern Oscillation |

FNO | Fourier Neural Operator |

FourCastNet | Fourier Forecasting Neural Network |

FVCOM | Finite-Volume Coastal Ocean Model |

GA | Genetic Algorithm |

GAN | Generative adversarial network |

GFD | Geophysical Fluid Dynamics |

GFS | Global Forecast System |

GP | Genetic Programming |

GPR | Gaussian Process Regression |

IAI | Interpretable AI |

JTWC | Joint Typhoon Warning Center |

JPM-OS | Joint probability method with optimized sampling methodology |

KGE | Kling-Gupta Efficiency |

KNMI | Royal Netherlands Meteorological Institute |

KNN | K-Nearest Neighbors |

LightGBM | Light Gradient Boosting Machine |

LSTM | Long Short-term Memory |

MAE | Mean Absolute Error |

MIMO | Multi-Input Multi-Output |

ML | Machine Learning |

MLP | Multilayer Perceptron |

MSE | Mean Squared Error |

NARX | Nonlinear AutoregRessive with eXogenous inputs |

NCEP | National Centers for Environmental Prediction |

NEMO | Nucleus for European Modelling of the Ocean model |

NNs | Neural Networks |

NS | Navier–Stokes |

NWP | Numerical Weather Prediction |

PCA | Principal Component Analysis |

PDEs | Partial Differential Equations |

PDP | Partial Dependence Plots |

PFI | Permuted Feature Importance |

PIML | Physics-Informed ML |

PINNs | Physics-Informed Neural Networks |

R^{2} | Coefficient of Determination |

ReLU | Rectified Linear Units |

ResNet | Residual Neural Network |

RF | Random Forest |

RMSE | Root Mean Squared Error |

RNN | Recurrent Neural Network |

ROMS | Regional Ocean Modeling System |

RSMC | Tokyo Regional Specialized Meteorological Center Tokyo |

SFS | Sequential Forward Selection |

SLOSH | Sea, Lake and Overland Surges from Hurricane model |

STWAVE | STeady State spectral WAVE |

SVM | Support Vector Machine |

SVR | Support Vector Regression |

SWAN | Simulating WAves Nearshore |

SWOT | Surface Water and Ocean Topography |

TC | Tropical Cyclone |

WAM | WAve Modeling |

WRF | Weather Research and Forecasting |

WW3 | WaveWatch III model |

XAI | eXplainable AI model |

XGBoost | eXtreme Gradient Boosting |

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**Figure 1.**The number of papers related to the application of ML in sea level/storm surge/coastal inundation forecasting collected by the authors before 2023 (bottom gradient bar chart). Timeline sketches of the development of Deep Learning (DL) in recent years (top orange) and some representative studies are marked within the circles [36,37,38,39]. GAN: Generative adversarial network, ResNet: Residual Neural Network, ChatGPT: Chat Generative Pre-Trained Transformer.

**Figure 2.**A schematic of the workflow of applying ML to develop a storm surge forecast product. Work starts with ‘Formulation of prediction problems’ and moves step by step following the filled arrows. The workflow is often iterative, with regular feedback and improvements to enhance the product’s performance and value. Dotted arrows mean returning to previous steps due to unsatisfying results.

**Figure 3.**Storm surge predictions in Shantou station with Mean (solid line) and (±) 95% confidence interval (shaded) across different lead times for Typhoon Peggy in 1986: (

**a**) t + 1; (

**b**) t + 2; (

**c**) t + 3; (

**d**) t + 6; (

**e**) t + 9; (

**f**) t + 12; (

**g**) t + 15; (

**h**) t + 18. To obtain the results, we tested each combination of typhoon parameters by conducting 30 experimental runs. The color of lines represents different combinations of parameters, e.g., S means using surge level data as inputs, SPL means using the data of surge levels, pressure and distance between TC center and target station as inputs, etc.

**Figure 4.**Storm surge predictions in Shantou station with Mean and (±) 95% confidence interval (error bar) across different lead times (from 1 h to 12 h) for Typhoon Peggy in 1986. Prediction performance in terms of (

**a**,

**d**) correlation coefficient (CC); (

**b**,

**e**) root mean square error (RMSE); (

**c**,

**f**) peak surge deviations ($\mathsf{\Delta}{S}_{p}$). To obtain the results, we tested each combination of typhoon parameters by conducting 30 experimental runs.

Formulation of Predicting Problems | Water Level Forecasting | Inundation Forecasting |
---|---|---|

Peak-value forecasting | [42,43] | |

Time-series forecasting | [50,51] | |

Spatio-temporal forecasting | [39,56,57,58] |

Study | Predictors | ||
---|---|---|---|

Typhoon Characteristics | Local Hydrodynamic Parameters | Local/Regional Meteorological Conditions | |

Sahoo and Bhaskaran [42] | Landfall location, approach angle, translation speed, maximum sustained wind speed | N/A ^{1} | N/A |

Kim et al. [44] | Longitude, latitude, central atmospheric pressure, wind speed near typhoon center, and surge level | Surge level | Wind speed, wind direction, sea-level pressure, drop of sea level pressure at five stations |

Al Kajbaf and Bensi [19] | Storm central pressure deficit, radius to maximum wind speed, forward velocity, heading direction, reference latitude and longitude | N/A | N/A |

Chen et al. [100] | Typhoon central pressure, central wind speed, moving speed, moving direction | Water level | Air pressure, wind speed, wind direction |

Lee et al. [52] | The time series of six TC parameters (latitude, longitude, heading direction, central pressure, radius of maximum winds, and translation speed). Beginning 30 h before passing the reference point and up to 9 h after passing the reference point | N/A | N/A |

Žust et al. [38] | N/A | Sea level (Tide and residual) | 10 m zonal and meridional winds, mean sea level pressure, air temperature at 2 m of the Adriatic basin |

Wei et al. [87] | Latitude, longitude, central pressure, distance between storm center and save point, radius of maximum winds, | Storm surge water level, storm-induced depth-averaged x-velocity, y-velocity | N/A |

Rus et al. [79] | N/A | Tide, sea surface height | 10 m zonal and meridional winds, mean sea level pressure of the Adriatic basin |

Xie et al. [48] | N/A | Previous 24-h sea level | Previous 6-h wind field data |

^{1}N/A: This stands for “Not Applicable”, showing that the data is not relevant in this study.

**Table 4.**The mean of three evaluation indices of storm surge predictions of typhoon Peggy with different combinations of input parameters based on the ANN model.

Combination | Index | S | SPL | SWL | SPWL | SPWLVI | SPWLVI + Lat&Lon |
---|---|---|---|---|---|---|---|

t + 1 | CC | 0.96 | 0.96 | 0.96 | 0.96 | 0.96 | 0.96 |

RMSE(cm) | 9.66 | 9.25 | 8.97 | 9.11 | 9.09 | 9.00 | |

$\mathsf{\Delta}{S}_{p}$(cm) | −8.01 | −1.14 | −4.99 | −1.42 | −4.43 | −4.10 | |

t + 2 | CC | 0.92 | 0.94 | 0.95 | 0.94 | 0.94 | 0.94 |

RMSE(cm) | 13.16 | 11.69 | 10.70 | 11.57 | 12.11 | 11.83 | |

$\mathsf{\Delta}{S}_{p}$(cm) | −17.74 | −2.01 | −7.66 | −2.15 | −4.94 | 3.24 | |

t + 3 | CC | 0.87 | 0.91 | 0.93 | 0.90 | 0.91 | 0.91 |

RMSE(cm) | 17.10 | 14.19 | 13.41 | 15.14 | 15.56 | 14.98 | |

$\mathsf{\Delta}{S}_{p}$(cm) | −26.36 | −6.32 | −18.96 | −7.51 | −13.35 | −0.83 | |

t + 6 | CC | 0.73 | 0.86 | 0.91 | 0.85 | 0.89 | 0.92 |

RMSE(cm) | 23.88 | 19.59 | 18.20 | 20.76 | 19.29 | 16.14 | |

$\mathsf{\Delta}{S}_{p}$(cm) | −45.86 | −38.43 | −35.75 | −33.82 | −41.90 | −21.68 | |

t + 9 | CC | 0.48 | 0.71 | 0.84 | 0.52 | 0.67 | 0.81 |

RMSE(cm) | 31.16 | 27.00 | 23.49 | 31.72 | 27.23 | 21.66 | |

$\mathsf{\Delta}{S}_{p}$(cm) | −64.97 | −62.24 | −47.63 | −40.32 | −55.18 | −15.55 | |

t + 12 | CC | 0.28 | 0.66 | 0.80 | 0.65 | 0.71 | 0.91 |

RMSE(cm) | 35.30 | 29.42 | 26.71 | 29.58 | 26.63 | 17.26 | |

$\mathsf{\Delta}{S}_{p}$(cm) | −66.04 | −74.60 | −66.89 | −62.02 | −49.78 | −20.64 | |

t + 18 | CC | 0.08 | 0.45 | 0.79 | 0.37 | 0.32 | 0.76 |

RMSE(cm) | 38.30 | 34.03 | 29.47 | 36.40 | 41.10 | 24.78 | |

$\mathsf{\Delta}{S}_{p}$(cm) | −76.56 | −76.77 | −70.86 | −47.65 | −31.40 | −27.65 | |

t + 24 | CC | 0.15 | 0.45 | 0.74 | 0.59 | 0.58 | 0.82 |

RMSE(cm) | 39.07 | 35.44 | 33.35 | 35.27 | 34.05 | 23.97 | |

$\mathsf{\Delta}{S}_{p}$(cm) | −83.90 | −77.66 | −80.70 | −76.76 | −64.36 | −28.83 |

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**MDPI and ACS Style**

Qin, Y.; Su, C.; Chu, D.; Zhang, J.; Song, J.
A Review of Application of Machine Learning in Storm Surge Problems. *J. Mar. Sci. Eng.* **2023**, *11*, 1729.
https://doi.org/10.3390/jmse11091729

**AMA Style**

Qin Y, Su C, Chu D, Zhang J, Song J.
A Review of Application of Machine Learning in Storm Surge Problems. *Journal of Marine Science and Engineering*. 2023; 11(9):1729.
https://doi.org/10.3390/jmse11091729

**Chicago/Turabian Style**

Qin, Yue, Changyu Su, Dongdong Chu, Jicai Zhang, and Jinbao Song.
2023. "A Review of Application of Machine Learning in Storm Surge Problems" *Journal of Marine Science and Engineering* 11, no. 9: 1729.
https://doi.org/10.3390/jmse11091729