# Climatology and Spatiotemporal Analysis of North Atlantic Rapidly Intensifying Hurricanes (1851–2017)

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

- To determine basin-wide and sub-basin frequency distributions and seasonality, with sub-basins organized into the North Atlantic, Gulf of Mexico, and Caribbean waterways (Figure 1).
- To examine potential trends in RI hurricane counts by utilizing a count time series regression model spanning the entire North Atlantic hurricane record (1851–2017) and shorter data subsets to assess possible data bias present in the trend.
- To analyze spatiotemporal trends of storms that both originate and initiate their RI cycle within the Gulf of Mexico basin compared to those in the North Atlantic.
- To examine spatiotemporal trends of storms that undergo more than one cycle of RI in their lifetime.
- To explore spatial trends that may exist within the sub-basins in regard to RI hurricane origins, RI genesis, RI landfall, and RI lifetime maximum intensity (LMI) points.

## 2. Experiments

#### 2.1. Data

^{−1}, this 6-h resolution can be considered too coarse for spatial analysis and modeling purposes [9]. Therefore, the hurricane data were interpolated hourly using splines for wind speed and the geographic position of the hurricane center, as detailed in Elsner and Jagger [9]. Utilizing this hourly interpolated data is advantageous due to the reduced likelihood of missing a hurricane passing through any given area [10].

^{−1}) (C), and landfall (D) points highlighted.

#### 2.2. Methods

#### 2.2.1. Time Series

_{i}’s) and p +1 parameters (β

_{i}’s). The model uses the logarithm of the rate as a response variable, but the regression structure is linear with the model coefficients determined by the method of maximum likelihood [9].

_{t}is white noise [15]. The ARCH(q) process specifies the conditional variance as a linear function of past sample variances only, whereas the GARCH(p,q) process also allows lagged conditional variances to enter [15]. This process was used when modeling the RI hurricane counts per year as a function of time in the regression equation

_{t}is the dependent variable of RI hurricane counts, and x

_{t}the explanatory variable of time, while b represents a vector of unknown parameters [15].

#### 2.2.2. Spatial and Temporal Clustering

_{h}of a univariate density f based on a random sample X

_{1},…,X

_{n}of size n is

## 3. Results

#### 3.1. Frequency and Seasonality

^{−1}higher, and the minimum windspeed of RI storms are more than 10 ms

^{−1}higher than non-RI storms. Table 2 lists the average LMI, minimum wind speed, maximum windspeed, and number of total storms for both groups of hurricanes.

#### 3.2. Time Series Analysis

#### 3.2.1. Entire Atlantic Basin

#### 3.2.2. North Atlantic Sub-Basin

#### 3.2.3. Gulf of Mexico Sub-Basin

#### 3.3. Spatial Cluster Analysis

#### 3.4. Temporal Cluster Analysis

## 4. Discussion and Concluding Remarks

^{−1}as compared to an average LMI of 48.27 ms

^{−1}for storms undergoing only one cycle of RI. This further corroborates the idea that the process of RI tends to spawn more intense and, thus, more dangerous, storms.

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Mercer, A.; Grimes, A. Atlantic Tropical Cyclone Rapid Intensification Probabilistic Forecasts from an Ensemble of Machine Learning Methods. Procedia Comp. Sci.
**2017**, 114, 333–340. [Google Scholar] [CrossRef] - Senkbeil, J.C.; Brommer, D.M.; Comstock, I.J. Tropical Cyclone Hazards in the USA. Geogr. Compass
**2011**, 5, 544–563. [Google Scholar] [CrossRef] - Kaplan, J.; Rozoff, C.M.; Demaria, M.; Sampson, C.R.; Kossin, J.P.; Velden, C.S. Evaluating Environmental Impacts on Tropical Cyclone Rapid Intensification Predictability Utilizing Statistical Models. J. Clim.
**2015**, 30, 1374–1396. [Google Scholar] [CrossRef] - Grimes, A.; Mercer, A. Synoptic-Scale Precursors to Tropical Cyclone Rapid Intensification in the Atlantic Basin. Adv. Meteorol.
**2015**, 2015, 1–16. [Google Scholar] [CrossRef] [Green Version] - Wang, C.; Wang, X.; Weisberg, R.H.; Black, M.L. Variability of tropical cyclone rapid intensification in the North Atlantic and its relationship with climate variations. Clim. Dyn.
**2017**, 49, 3627–3645. [Google Scholar] [CrossRef] - Yaukey, P.H. Intensification and rapid intensification of North Atlantic tropical cylones: Geography, time of year, age since genesis, and storm characteristics. Int. J. Climatol.
**2013**, 34, 1038–1049. [Google Scholar] [CrossRef] - Xu, J.; Wang, Y. A Statistical Analysis on the Dependence of Tropical Cyclone Intensification Rate on the Storm Intensity and Size in the North Atlantic. Weather Forecast.
**2015**, 30, 692–701. [Google Scholar] [CrossRef] - Landsea, C.W.; Franklin, J.L. Atlantic Hurricane Database Uncertainty and Presentation of a New Database Format. Mon. Weather Rev.
**2013**, 141, 3576–3592. [Google Scholar] [CrossRef] - Elsner, J.B.; Jagger, T.H. Hurricane Climatology: A Modern Statistical Guide Using R; Oxford University Press: New York, NY, USA, 2013. [Google Scholar]
- Malmstadt, J.C.; Elsner, J.B.; Jagger, T.H. Risk of Strong Hurricane Winds to Florida Cities. J. Appl. Meteor. Climatol.
**2010**, 49, 2121–2132. [Google Scholar] [CrossRef] - Thom, H.C.S. The Distribution of Annual Tropical Cyclone Frequency. J. Geophys. Res.
**1960**, 65, 213–222. [Google Scholar] [CrossRef] - Russell, L.R. Probability Distributions for Hurricane Effects. J. Waterw. Harb. Coast. Eng. Div.
**1971**, 97, 139–154. [Google Scholar] - Elsner, J.B.; Jagger, T.H. Prediction Models for Annual U.S. Hurricane Counts. J. Clim.
**2006**, 19, 2935–2952. [Google Scholar] [CrossRef] - Liboschik, T. Modeling Count Time Series Following Generalized Linear Models. Ph.D. Dissertation, TU Dortmund University, Dortmund, Germany, 13 July 2016. [Google Scholar]
- Bollerslev, T. Generalized Autoregressive Conditional Heteroskedasticity. J. Econom.
**1986**, 31, 307–327. [Google Scholar] [CrossRef] [Green Version] - Baddeley, A.; Turner, R. Spatstat: An R Package for Analyzing Spatial Point Patterns. J. Stat. Softw.
**2005**, 12, 1–42. [Google Scholar] [CrossRef] [Green Version] - Sheather, S.J.; Jones, M.C. A Reliable Data-based Bandwidth Selection Method for Kernel Density Estimation. J. R. Stat. Soc. B
**1991**, 53, 683–690. [Google Scholar] [CrossRef] - R Core Team. R: A Language and Environment for Statistical Computing; R Foundation for Statistical Computing: Vienna, Austria, 2013; Available online: https://www.R-project.org/ (accessed on 1 December 2018).
- Perlroth, I. Hurricane Behavior as Related to Oceanographic and Environmental Conditions. Tellus
**1967**, 19, 258–268. [Google Scholar] [CrossRef] - Hamill, T.M. Interpretation of Rank Histograms for Verifying Ensemble Forecasts. Mon. Weather Rev.
**2001**, 129, 550–560. [Google Scholar] [CrossRef] - Gneiting, T.; Balabdaoui, F.; Raftery, A.E. Probabilistic Forecasts, calibration, and sharpness. J. R. Stat. Soc. B
**2007**, 69, 243–268. [Google Scholar] [CrossRef] [Green Version] - Tallapragada, V.; Kieu, C.; Kwon, Y.; Trahan, S.; Liu, Q.; Zhang, Z.; Kwon, I.H. Structural Evaluation of the HWRF model during 2011 model implementation. Mon. Weather Rev.
**2013**, 142, 4308–4325. [Google Scholar] [CrossRef] - Tallapragada, V.; Kieu, C.; Trahan, S.; Liu, Q.; Wang, W.; Zhang, Z.; Strahl, B. Real-Time Forecasts for the 2012 North-Western Pacific Typhoon Season using the NCEP Operational HWRF. Weather Forecast.
**2015**, 30, 1355–1373. [Google Scholar] [CrossRef] - Jarvinen, B.R.; Neumann, C.J.; Davis, M.A.S. A Tropical Cyclone Data Tape for the North Atlantic Basin, 1886–1983: Contents, Limitations, and Uses. NOAA Tech. Memo. NWS NHC
**1984**, 22, 1–21. [Google Scholar]

**Figure 2.**Schematic of defined rapid intensification (RI) hurricane processes using Hurricane Camille’s track in 1969 as an example. (

**A**) Hurricane origin point, (

**B**) RI genesis point, (

**C**) lifetime maximum intensity (LMI) point, and (

**D**) landfall point.

**Figure 3.**Monthly frequency distribution of North Atlantic (black) and Gulf of Mexico (gray) sub-basin RI counts of storms originating within each basin.

**Figure 4.**Histograms of rapidly intensifying hurricane counts per year from (

**a**) 1851–2017, (

**b**) 1900–2017, and (

**c**) 1950–2017.

**Figure 5.**Probable integral transform (PIT) histogram testing for data uniformity of the generalized autoregressive conditional heteroscedasticity (GARCH) time series count model.

**Figure 6.**Incidence rate ratio showing (

**a**) a 2% increase of hurricanes undergoing more than one cycle of RI in their lifetimes from 1851–2017, (

**b**) a 1.5% increase of hurricanes undergoing more than one cycle of RI from 1900–2017, and (

**c**) a 0.7% increase of hurricanes undergoing more than one cycle of RI from 1950–2017.

**Figure 7.**Incidence rate ratios of RI storms originating within the North Atlantic sub-basin over time described by the Poisson regression model (

**a**) between 1851–2017 and (

**b**) depicting 1900–2017 and (

**c**) a 0.4% factor increase from 1950 to 2017.

**Figure 8.**Incidence rate ratios of RI storms initiating RI within the North Atlantic sub-basin over time described by the Poisson regression model (

**a**) between 1851–2017, (

**b**) depicting 1900–2017, and (

**c**) 1950–2017.

**Figure 9.**Incidence rate ratios of RI storms originating within the Gulf of Mexico sub-basin over time described by the Poisson regression model (

**a**) between 1851–2017, (

**b**) depicting 1900–2017, and (

**c**) 1950–2017.

**Figure 10.**Incidence rate ratios of RI storms initiating RI within the Gulf of Mexico sub-basin over time described by the Poisson regression model (

**a**) between 1851–2017, (

**b**) depicting 1900–2017, and (

**c**) 1950–2017.

**Figure 11.**(

**a**) Kernel density analysis of RI hurricanes at their origin points (1851–2017). (

**b**) Generalization of K graph for inhomogeneous data with the empirical (black) curve above the theoretical (red) curve for lag distances less than 150 km, indicating the likelihood of clustering up to this distance.

**Figure 12.**(

**a**) Kernel density analysis of RI hurricanes at their initial RI genesis points (1851–2017). (

**b**) Generalization of K graph for inhomogeneous data of initial RI genesis points with the empirical (black) curve above the theoretical (red) curve for lag distances of 150 km and lower, indicating the likelihood of clustering up to this distance.

**Figure 13.**(

**a**) Kernel density analysis of RI hurricanes at their initial RI completion points (1851–2017). (

**b**) Generalization of K graph for inhomogeneous data of initial RI completion points with the empirical (black) curve above the theoretical (red) curve for lag distances 500 km and lower, indicating the likelihood of clustering for all distances up to this point.

**Figure 14.**(

**a**) Kernel density analysis of RI hurricanes at their landfall points (1851–2017). (

**b**) Generalization of K graph for inhomogeneous data of RI landfall points with the empirical (black) curve above the theoretical (red) curve until a 750-km lag distance and the theoretical curve over the empirical curve for all of the following lag distances.

**Figure 17.**Generalization of K graph for inhomogeneous data of RI LMI points with the empirical (black) curve above the theoretical (red) curve to a lag distance of 350 km, indicating significant clustering up to this point of distance between hurricanes.

**Figure 18.**Tracks of the five storms that underwent 4 RI cycles with their intensity delineated by darkening red shades. (Beulah (1967), Camille (1969), Allen (1980), Gilbert (1988), and Emily (2005)).

**Table 1.**Comparison of Gulf of Mexico, North Atlantic, and Caribbean rapid intensification (RI) storm origins and RI genesis sites.

Sub-Basin | No. of RI Storm Origins | No. of RI Genesis Points |
---|---|---|

Gulf of Mexico | 79 | 113 |

North Atlantic | 178 | 153 |

Caribbean Sea | 135 | 126 |

**Table 2.**Comparison of the number, average lifetime maximum intensity (LMI), minimum wind speed, and maximum windspeed of RI hurricanes and non-RI hurricanes. Category refers to the Saffir-Simpson scale.

Type of Storm | No. of Total Storms | Average LMI (ms^{−1}) | Minimum Wind Speed (ms^{−1}) | Maximum Wind Speed (ms^{−1}) |
---|---|---|---|---|

RI Storms | 392 | 52.02 | 28.34 | 83.8 (Cat 5) |

Non-RI Storms | 1226 | 32.64 | 17.51 | 71.88 (Cat 5) |

1 RI Cycle | 2 RI Cycles | 3 RI Cycles | 4 RI Cycles |
---|---|---|---|

300 | 75 | 12 | 5 |

**Table 4.**Time series count model coefficients and confidence intervals within a Poisson distribution.

Years | Beta_1 Coefficient | CI (lower) | CI (upper) |
---|---|---|---|

1851–2017 | 0.483 | 0.36 | 0.606 |

1900–2017 | 0.291 | 0.136 | 0.447 |

1950–2017 | 9.84^{−11} | −0.232 | 0.232 |

**Table 5.**Coefficient estimates, p-values, and chi-square p-values on the residual deviance for RI storms originating within the North Atlantic sub-basin.

Years | Coefficient Estimate | p-Value | Chi-Square Value |
---|---|---|---|

1851–2017 | 0.013 | <0.000 | 0.008 |

1900–2017 | 0.012 | <0.000 | 0.010 |

1950–2017 | 0.005 | 0.180 | 0.04 |

**Table 6.**Coefficient estimates, p-values, and chi-square p-values on the residual deviance for RI storms initiating their first cycle of RI within the North Atlantic sub-basin.

Years | Coefficient Estimate | p-Value | Chi-Square Value |
---|---|---|---|

1851–2017 | 0.013 | <0.000 | 0.05 |

1900–2017 | 0.012 | <0.000 | 0.03 |

1950–2017 | 0.004 | 0.262 | 0.19 |

**Table 7.**Coefficient estimates, p-values, and chi-square p-values on the residual deviance for RI storms originating within the Gulf of Mexico sub-basin.

Years | Coefficient Estimate | p-Value | Chi-Square Value |
---|---|---|---|

1851–2017 | 0.009 | <0.000 | 0.700 |

1900–2017 | 0.009 | 0.02 | 0.473 |

1950–2017 | -0.007 | 0.278 | 0.321 |

**Table 8.**Coefficient estimates, p-values, and chi-square p-values on the residual deviance for RI storms initiating their first cycle of RI within the Gulf of Mexico sub-basin.

Years | Coefficient Estimate | p-Value | Chi-Square Value |
---|---|---|---|

1851–2017 | 0.010 | <0.000 | 0.375 |

1900–2017 | 0.009 | 0.004 | 0.282 |

1950–2017 | -0.003 | 0.670 | 0.149 |

**Table 9.**Observed (O) and expected (E) number of years with zero hurricanes and with 3+ hurricanes originating (o) and initiating RI (i) within the Gulf of Mexico, Caribbean, and Atlantic sub-basins.

Region | O(= 0) | E(= 0) | O(≥ 3) | E(≥ 3) | Chi-Square Statistic | p-Value |
---|---|---|---|---|---|---|

Gulf of Mexico_{o} | 107 | 104.7 | 1 | 2.0 | 0.59 | 0.75 |

Caribbean_{o} | 86 | 74.4 | 13 | 8.1 | 7.94 | 0.02 |

Atlantic_{o} | 47 | 25.5 | 49 | 48.6 | 23.37 | <0.00 |

Gulf of Mexico_{i} | 89 | 85.4 | 9 | 5.1 | 3.82 | 0.15 |

Caribbean_{i} | 88 | 78.5 | 12 | 6.9 | 7.60 | 0.02 |

Atlantic_{i} | 50 | 31.2 | 44 | 39.5 | 212.2 | <0.00 |

Multi-RI Hurricanes | 107 | 96.3 | 7 | 3.1 | 9.29 | 0.01 |

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**MDPI and ACS Style**

Benedetto, K.M.; Trepanier, J.C.
Climatology and Spatiotemporal Analysis of North Atlantic Rapidly Intensifying Hurricanes (1851–2017). *Atmosphere* **2020**, *11*, 291.
https://doi.org/10.3390/atmos11030291

**AMA Style**

Benedetto KM, Trepanier JC.
Climatology and Spatiotemporal Analysis of North Atlantic Rapidly Intensifying Hurricanes (1851–2017). *Atmosphere*. 2020; 11(3):291.
https://doi.org/10.3390/atmos11030291

**Chicago/Turabian Style**

Benedetto, Kathleen M., and Jill C. Trepanier.
2020. "Climatology and Spatiotemporal Analysis of North Atlantic Rapidly Intensifying Hurricanes (1851–2017)" *Atmosphere* 11, no. 3: 291.
https://doi.org/10.3390/atmos11030291