# Predicting Atlantic Hurricanes Using Machine Learning

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## Abstract

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## 1. Introduction

^{−3}, which, in their way, change the properties of clouds and the evolution and development of precipitation [26,27]. It also modulates Caribbean storms [2] and modifies the climate by absorbing and dispersing solar radiation. Together with other internal and external factors of the ocean-atmosphere system, such as winds and clouds [28], African dust provokes a decrease in the ocean surface temperature, affecting the genesis of Atlantic tropical hurricanes [29] by inhibiting their formation [23]. Tons of dust from the desert is transported by the winds over thousands of kilometers of the atmosphere. This dust interacts chemically with the clouds and radiation to modify the climate, while acting against global warming. The amount of dust increased considerably by the end of the 1960s and beginning of the 1970s, when there was a severe drought in North Africa. Present climatic models that include African dust have shown that the variability of African dust is an important factor in predicting climatic change.

## 2. Data and Methods

#### 2.1. Wavelet Spectral Analysis

#### 2.2. Inverse Wavelet Spectral Analysis

#### 2.3. Machine Learning Algorithms for Forecasting Hurricane Activity

#### 2.3.1. Non-Linear Autoregressive eXogenous (NARX) Model

#### 2.3.2. Algorithms for the Estimation of the Following High or Active Phase of Hurricane Activity

- I.
- Use wavelet transform (Equation (2)) to find the periodicities (hurricane activity patterns) for each of the Atlantic hurricane categories analyzed.
- II.
- The decomposition of the hurricane records in time series called “channels” with the periodicities obtained in step (I) can next be obtained using the inverse wavelet (Equation (3)).
- III.
- Selection of lags Q and P in the exogenous input and output data, respectively.
- IV.
- Use a Radial Basis Function (RBF) kernel. The RBF has various forms: (a) Gaussian function, (b) logistic function (or reflected sigmoid function), and (c) inverse quadratic function. We have selected the Gaussian function as RBF. The user may select any of the radial functions and similar results will be obtained.
- V.
- For training, validation, testing and deduction of the hyper-parameters of the model. Use the K-fold cross-validation. Set aside $1/K$ of data. Train the model with the remaining $(K-1)/K$ data. Measure the accuracy obtained on the $1/K$ data that we had set aside. K independent training is therefore acquired. The final accuracy will be the average of the previous K accuracies. Note that we are hiding a $1/K$ part of the training set during each iteration. This is applied at the time of training. After these K iterations, we obtain K accuracies that should be similar to each other; this would be an indicator whether the model is working well or not. In this work, we used $K=10$, but it is possible to vary K between 5 and 10.
- VI.
- Determination of the weight and bias.
- VII.
- Estimation of next high cycle of hurricane activity using Equation (5).
- VIII.
- Computation of a cost function.
- IX.
- Test of the accuracy of the estimate next high cycle of hurricane activity.
- X.
- Test of the cost function. We have used the mean squared error (MSE). If this function was small enough, stop and go to the next step. Otherwise, we change one of the parameters P and/or Q and repeat from step (III) onwards.
- XI.
- Use the wavelet transform to help determine if the periodicities of the estimated high hurricane activity have the same periodicities obtained in step (I). If yes, then with these new data (i.e., with the input data and these new hurricane cycles), go to step (VII) to calculate the next hurricane cycles. Otherwise, repeat step (VI).

#### 2.4. Geospatial Information Mapping

## 3. Results

#### 3.1. Category 5 Atlantic Hurricanes

#### 3.1.1. Spectral Analysis

#### 3.1.2. Machine Learning Model of Category 5 Atlantic Hurricanes

#### 3.2. Category 4 Atlantic Hurricanes

#### 3.2.1. Spectral Analysis

#### 3.2.2. Machine Learning Model of Category 4 Atlantic Hurricanes

#### 3.3. Category 3 Atlantic Hurricanes

#### 3.3.1. Spectral Analysis

#### 3.3.2. Machine Learning Model of Category 3 Atlantic Hurricanes

#### 3.4. Category 2 Atlantic Hurricanes

#### 3.4.1. Spectral Analysis

#### 3.4.2. Machine Learning Model of Category 2 Atlantic Hurricanes

#### 3.5. Spatial Distribution of Atlantic Hurricanes

## 4. Discussion and Conclusions

^{3}-HITS), can be used see [50,51]. Ultimately, our work highlights that the multiannual and decadal variations (trends) of Atlantic hurricanes from categories 2 to 5 are stable and consistent from 1950 to 2021 which can be assumed to be the result of the more persistent and coherent interactions of the coupled atmosphere-ocean-geographical system in affecting and modulating the tropical hurricanes. This notable property is indeed a useful signal from the point of view of signal theory and proffers a probabilistic forecast as we have performed in this study.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

NOAA | National Oceanic and Atmospheric Administration |

ENSO | El Nino-Southern Oscillation |

AMO | Atlantic Multidecadal Oscillation |

WT | wavelet transform |

NARX | Non-linear Autoregressive eXogenous |

LS-SVM | Least-Squares Support-Vector Machines |

ML | Machine Learning |

RBF | radial basis function |

GIS | geographic information system |

GEBCO | General Bathymetric Chart of the Oceans |

NAO | North Atlantic Oscillation |

TSI | total solar irradiance |

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**Figure 1.**Time-frequency wavelet results of category 5 Atlantic hurricanes between 1950 and 2021. The digital time series for category 5 Atlantic hurricanes is shown in the upper panel. The global wavelet spectrum is shown in the left panel. The central panel shows the calculated wavelet Power Spectral Density (PSD) in normalized units adopting the red-green-blue color scales. The Cone Of Influence (COI, “U”-shaped curve with shaded outer zones) shows the possible edge effects in the PSD. The time-frequency regions with wavelet spectral power detection above 95% confidence level are marked with thin black contours.

**Figure 2.**Probabilistic hindcasts and forecasts for the category 5 Atlantic hurricanes. Bayesian inference of the LS-SVM model (blue line and shade) compared with the historical category 5 Atlantic hurricanes (purple vertical bars) clustered in 8 groups (I–VIII). In addition, the probabilistic prediction of category 5 Atlantic hurricane is shown for the following period (cluster IX). The blue shaded area represents the 95% confidence intervals of the Bayesian model.

**Figure 3.**Time-frequency wavelet results of category 4 Atlantic hurricanes between 1950 and 2021. The digital time series for category 4 Atlantic hurricanes is shown in the upper panel. The global wavelet spectrum is shown in the left panel. The central panel shows the calculated wavelet Power Spectral Density (PSD) in normalized units adopting the red-green-blue color scales. The Cone Of Influence (COI, “U”-shaped curve with shaded outer zones) shows the possible edge effects in the PSD. The time-frequency regions with wavelet spectral power detection above 95% confidence level are marked with thin black contours.

**Figure 4.**Probabilistic hindcasts and forecasts for the category 4 Atlantic hurricanes. Bayesian inference of the LS-SVM model (blue line and shade) compared with the historical category 4 Atlantic hurricanes (purple vertical bars) clustered in 15 groups (I–XV). In addition, the probabilistic prediction for category 4 Atlantic hurricane is shown for the following period (cluster XVI). The blue shaded area represents the 95% confidence intervals of the Bayesian model.

**Figure 5.**Time-frequency wavelet results of category 3 Atlantic hurricanes between 1950 and 2021. The digital time series for category 3 Atlantic hurricanes is shown in the upper panel. The global wavelet spectrum is shown in the left panel. The central panel shows the calculated wavelet Power Spectral Density (PSD) in normalized units adopting the red-green-blue color scales. The Cone Of Influence (COI, “U”-shaped curve with shaded outer zones) shows the possible edge effects in the PSD. The time-frequency regions with wavelet spectral power detection above 95% confidence level are marked with thin black contours.

**Figure 6.**Probabilistic hindcasts and forecasts for the category 3 Atlantic hurricanes. Bayesian inference of the LS-SVM model (blue line and shade) compared with the historical category 3 Atlantic hurricanes (purple vertical bars) clustered in 16 groups (I–XVI). In addition, the probabilistic earthquake prediction is shown for the following period (cluster XVII). The blue shaded area represents the 95% confidence intervals of the Bayesian model.

**Figure 7.**Time-frequency wavelet results of category 2 Atlantic hurricanes between 1950 and 2021. The digital time series for category 2 Atlantic hurricanes is shown in the upper panel. The global wavelet spectrum is shown in the left panel. The central panel shows the calculated wavelet Power Spectral Density (PSD) in normalized units adopting the red-green-blue color scales. The Cone Of Influence (COI, “U”-shaped curve with shaded outer zones) shows the possible edge effects in the PSD. The time-frequency regions with wavelet spectral power detection above 95% confidence level are marked with thin black contours.

**Figure 8.**Probabilistic hindcasts and forecasts for the category 2 Atlantic hurricane. Bayesian inference of the LS-SVM model (blue line and shade) compared with the historical category 2 Atlantic hurricanes (purple vertical bars) clustered in 18 groups (I–XVIII). In addition, the probabilistic earthquake prediction is shown for the following period (cluster XIX). The blue shaded area represents the 95% confidence intervals of the Bayesian model.

**Figure 9.**Speed distribution map of Atlantic hurricanes for each of the categories: (

**a**) Category 2; (

**b**) Category 3; (

**c**) Category 4 where the main zone (marked by the rectangular box) of cyclogenesis seems to fall outside the Gulf of Mexico. In addition, in panel (

**d**) we show the region of cyclogenesis for Category 5 Atlantic hurricanes that highlights five areas of concentration around (I) the east coast of the United States, (II) the Northeast of Mexico, (III) the Caribbean Sea, (IV) the Central American coast, and (V) the north of the Greater Antilles.

**Figure 10.**Probability distribution maps for the Atlantic hurricane wind speed for: (

**a**) Category 2; (

**b**) Category 3; (

**c**) Category 4; (

**d**) Category 5. The vertical and horizontal lines indicate the local maxima for the longitudinal and latitudinal distributions, respectively. The main point of this spatial clustering map is to indicate the possible connection between the climatic and geographical conditions for the development of maximum speed of Atlantic hurricanes.

**Figure 11.**Category-5 Hurricane Wilma (2006). (

**a**) This is an example of the analysis of the category-5 hurricane Wilma wind speed and bathymetry. It reaches its maximum speed (black line) around the greatest depth (−4500 m; dotted blue line). (

**b**) It is also possible to analyze the atmospheric pressure data for the same example of Wilma. It reaches its minimum pressure (black line) around the greatest depth (−4500 m; dotted blue line).

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## Share and Cite

**MDPI and ACS Style**

Herrera, V.M.V.; Martell-Dubois, R.; Soon, W.; Velasco Herrera, G.; Cerdeira-Estrada, S.; Zúñiga, E.; Rosique-de la Cruz, L. Predicting Atlantic Hurricanes Using Machine Learning. *Atmosphere* **2022**, *13*, 707.
https://doi.org/10.3390/atmos13050707

**AMA Style**

Herrera VMV, Martell-Dubois R, Soon W, Velasco Herrera G, Cerdeira-Estrada S, Zúñiga E, Rosique-de la Cruz L. Predicting Atlantic Hurricanes Using Machine Learning. *Atmosphere*. 2022; 13(5):707.
https://doi.org/10.3390/atmos13050707

**Chicago/Turabian Style**

Herrera, Victor Manuel Velasco, Raúl Martell-Dubois, Willie Soon, Graciela Velasco Herrera, Sergio Cerdeira-Estrada, Emmanuel Zúñiga, and Laura Rosique-de la Cruz. 2022. "Predicting Atlantic Hurricanes Using Machine Learning" *Atmosphere* 13, no. 5: 707.
https://doi.org/10.3390/atmos13050707