Wind speed analysis of hurricane Sandy

atmosphere Article Wind Speed Analysis of Hurricane Sandy Pablo Martínez, Isidro A. Pérez * , María Luisa Sánchez, María de los Ángeles García and Nuria Pardo   Citation: Martínez, P.; Pérez, I.A.; Sánchez, M.L.; García, M.d.l.Á.; Pardo, N. Wind Speed Analysis of Hurricane Sandy. Atmosphere 2021,12, 1480. https://doi.org/10.3390/ atmos12111480 Academic Editor: Joshua Cossuth Received: 20 October 2021 Accepted: 4 November 2021 Published: 9 November 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). Department of Applied Physics, Faculty of Sciences, University of Valladolid, Paseo de Belén, 7, 47011 Valladolid, Spain; [email protected] (P.M.); [email protected] (M.L.S.); [email protected] (M.d.l.Á.G.); npar[email protected] (N.P.) *Correspondence: iaper[email protected]; Tel.: +34-983-184-189 Abstract: The database of the HWind project sponsored by the National Oceanic and Atmospheric Administration (NOAA) for hurricanes between 1994 and 2013 is analysed. This is the first objective of the current research. Among these hurricanes, Hurricane Sandy was selected for a detailed study due to the number of files available and its social relevance, with this being the second objective of this study. Robust wind speed statistics showed a sharp increase in wind speed, around 6 m s −1 at the initial stage as Category 1, and a linear progression of its interquartile range, which increased at a rate of 0.54 m s −1 per day. Wind speed distributions were initially right-skewed. However, they evolved to nearly symmetrical or even left-skewed distributions. Robust kurtosis was similar to that of the Gaussian distribution. Due to the noticeable fraction of wind speed intermediate values, the Laplace distribution was used, its scale parameter increasing slightly during the hurricane’s lifecycle. The key features of the current study were the surface and recirculation factor calculation. The surface area with a category equal to, or higher than, a tropical storm was calculated and assumed to be circular. Its radius increased linearly up to 600 km. Finally, parcel trajectories were spirals in the lower atmosphere but loops in the mid-troposphere due to wind translation and rotation. The recirculation factor varied, reaching values close to 0.9 and revealing atmospheric stratification. Keywords: wind statistics; wind field; tropical cyclone; air parcel trajectory; recirculation factor 1. Introduction Hurricanes are among the most destructive natural hazards, not only in terms of human life, but also on built infrastructure [ 1 ]. Since their consequences are devastating, the effects of these winds on structures such as bridges, transmission lines, offshore wind turbines, skyscrapers, or water supplies are the subject of research [ 2 – 6 ]. However, the most common constructions are usually low-rise buildings, where the direct impact perceived by most of the population is on the building roofs [ 7 ]. Moreover, coastal economic activities, such as fisheries, are affected [ 8 ]. Last but not least, the longest-lasting consequences are observed on human health [9]. Due to their global impact, hurricanes have been studied in numerous analyses, some of which, such as the relationship between pressure or temperature and wind, are experimentally based [ 10 , 11 ]. Other studies consider the vertical wind profile [ 12 ], which is extremely useful for evaluating the structural safety of buildings in extreme wind conditions. The hurricane trajectory analysis is one line of research [ 13 ], with other studies focus on gauging their size [ 14 ]. Theoretical research has also occasionally been conducted [15]. Duetothecloselinkbetweenoceansurfacetemperaturesandhurricanes, Hosseini et al. [16] obtained a high correlation between sea surface temperature, the increase in which was attributed to climate change, and hurricane frequency over the last century. Another consequence of recent atmospheric warming might be the decrease in translation speed and the increase in the rain rate [ 17 ]. However, Rojo-Garibaldi et al. [ 18 ] reported a decreasing Atmosphere 2021,12, 1480. https://doi.org/10.3390/atmos12111480 https://www.mdpi.com/journal/atmosphere Atmosphere 2021,12, 1480 2 of 13 trend in the number of hurricanes in the Gulf of Mexico and the Caribbean over a wider period, 1749–2010, which they correlated with sunspot activity. The current paper is divided into two unequal sections. The first analyses a hurricane database spanning a period of nearly twenty years in order to explore its main features and hurricane distributions, with the extended analysis period being one of the prominent aspects in this section. The remainder of the research is devoted to Hurricane Sandy, which hit in October 2012 and gained prominence due to its trajectory, which ran parallel to the US coast, sparking tremendous fear in much of the population. Its origin was traced to a Saharan dust event on 8 October 2012 that moved west until cyclogenesis conditions were reached over the Caribbean [ 19 ]. Its evolution was affected by polar and subtropical jet streams [ 20 ]. Finally, the “Greenland block”, a high-pressure area near Greenland, turned the hurricane towards the northwest coast of the United States [ 21 ]. This left turn was unusual [ 22 ] and the wind intensified due to a warm seclusion phase [ 23 ]. Its effects, such as moderate flooding and sand deposition [ 24 ] or soil contamination [ 25 ], were noticeable on the coast. However, water clarity and nutrients reached pre-storm conditions in about one year on the Hudson–Raritan estuary, whereas biotic recovery took longer than that in other estuaries [ 26 ]. Recent analyses of this hurricane have focused on its reintensification after its extratropical transition [ 27 ], its roll vortices, which were a prominent feature due to their large wavelengths [ 28 ], its surges [ 29 , 30 ], its effects on infrastructures [ 31 ], and its westward turn when it made landfall [ 32 , 33 ]. In the second section of this paper, modelled wind fields are used to explore the progression of wind statistics and the hurricane size. As a specific contribution of this research, this area is determined by plotting isotachs. Finally, since air parcel trajectories are spirals or similar, the evolution of the recirculation factor is studied, with the analysis of this factor being another original contribution of this research. 2. Materials and Methods 2.1. Database Description Files considered in the current research correspond to the HWind Project [ 34 , 35 ], which are freely available [ 36 ]. This database extended mainly from 1994 to 2013, covering over 200 hurricanes. The information for each hurricane includes real-time observations and maps with the wind field and wind speed components in a grid, where the origin lies in the hurricane centre. These latter files were used in this paper. One section of this study is devoted to analysing air parcel trajectories. These trajectories were calculated with the METeorological data EXplorer (METEX) model [ 37 ], which provides, among other variables, the hourly longitude and latitude of the air parcel one day before it reaches the desired point. 2.2. Statistics Wind fields are described using robust statistics. The median, Q 0.5 , is considered as the location. Spread is quantified by the interquartile range, IQR = Q 0.75 − Q 0.25 , where Q 0.25 and Q 0.75 are the first and third quartiles, respectively. Symmetry is determined by the Yule-Kendall index, γYK [38] γYK =(Q0.25 −2Q0.5 +Q0.75)/IQR (1) Finally, the distribution flatness is given by the robust kurtosis, RK [39] RK =(Q0.75 −Q0.25)/[2(D0.9 −D0.1)], (2) where D 0.1 , and D 0.9 are the first and ninth deciles, respectively. RK is 0.263 for a Gaussian distribution. Atmosphere 2021,12, 1480 3 of 13 2.3. The Laplace Distribution Its probability density function, f, is defined as f(x)=1/(2b)exp(−|x−Q0.5|/b), (3) where the median is the location parameter, and bis the scale parameter, and b=1/n∑n i=1|xi−Q0.5|, (4) where nis the number of xi, which are the wind speed values of each wind field. 2.4. Recirculation Factor This factor was introduced by Allwine and Whiteman [ 40 ] to indicate the presence of recirculation on a given timescale, usually one day. Figure 1a illustrates its calculation. The air parcel moves from point B, with longitude λ1 and latitude ϕ1 , to point A( λ0 , ϕ0 ). Siis the distance travelled by the air parcel each hour, and the wind run, S, is its sum. S=∑24 i=1Si, (5) Atmosphere 2021, 12, x FOR PEER REVIEW 3 of 13 where the median is the location parameter, and b is the scale parameter, and 𝑏=1 𝑛 ⁄ ∑| 𝑥−𝑄 .|   , (4) where n is the number of xi, which are the wind speed values of each wind field. 2.4. Recirculation Factor This factor was introduced by Allwine and Whiteman [40] to indicate the presence of recirculation on a given timescale, usually one day. Figure 1a illustrates its calculation. The air parcel moves from point B, with longitude λ1 and latitude 𝜑, to point A(λ0, 𝜑). Si is the distance travelled by the air parcel each hour, and the wind run, S, is its sum. 𝑆=∑𝑆   , (5) Transport distance, L, is the straight distance between the beginning, B, and end of trajectory, A, and the recirculation factor is 𝑅=1−𝐿 𝑆 ⁄, (6) which lies between 0 and 1. Since Si and L are arcs on the Earth’s surface, these distances are calculated by the Sinnott equation [41], which for arc L is 𝑠𝑖𝑛󰇛𝐿2 ⁄󰇜 =󰇝𝑠𝑖𝑛󰇟󰇛𝜑−𝜑 󰇜2 ⁄󰇠 + cos 𝜑cos 𝜑 𝑠𝑖𝑛 󰇟󰇛𝜆−𝜆 󰇜2 ⁄󰇠󰇞  ⁄ (7) R equal to 0 means no recirculation, since the trajectory is a straight line. However, when R is equal to 1, the air parcel has returned to its origin. Figure 1b presents different recirculation factors assuming that the corresponding trajectories are circumference arcs. Figure 1. (a) An example of one-day backward trajectory from B to A, together with the transport distance L. The wind run is the addition of distances Si. (b) Recirculation factors when the trajectories from B to A are circumference arcs. In this figure, AB is the transport distance. The lowest value of the recirculation factor corresponds to the run from A to B following a straight line. When the arc increases, so does the recirculation factor. 3. Results 3.1. Database Analysis Figure 2a presents the distribution of 241 hurricanes recorded in the period 1994– 2013. Most correspond to the Atlantic Basin (84.23%), followed by the East Pacific Basin (14.11%) and the West Pacific Basin (1.66%). If the first year (1994) is excluded, the average number is 12.6 hurricanes per year. This is in sharp contrast to 2004, this being the year Figure 1. ( a ) An example of one-day backward trajectory from B to A, together with the transport distance L. The wind run is the addition of distances S i. ( b ) Recirculation factors when the trajectories from B to A are circumference arcs. In this figure, AB is the transport distance. The lowest value of the recirculation factor corresponds to the run from A to B following a straight line. When the arc increases, so does the recirculation factor. Transport distance, L, is the straight distance between the beginning, B, and end of trajectory, A, and the recirculation factor is R=1−L/S, (6) which lies between 0 and 1. Since S i and Lare arcs on the Earth’s surface, these distances are calculated by the Sinnott equation [41], which for arc Lis sin(L/2)=nsin2[(ϕ0−ϕ1)/2]+cos ϕ0cos ϕ1sin2[(λ0−λ1)/2]o1/2 (7) Atmosphere 2021,12, 1480 4 of 13 Requal to 0 means no recirculation, since the trajectory is a straight line. However, when Ris equal to 1, the air parcel has returned to its origin. Figure 1b presents different recirculation factors assuming that the corresponding trajectories are circumference arcs. 3. Results 3.1. Database Analysis Figure 2a presents the distribution of 241 hurricanes recorded in the period 1994–2013. Most correspond to the Atlantic Basin (84.23%), followed by the East Pacific Basin (14.11%) and the West Pacific Basin (1.66%). If the first year (1994) is excluded, the average number is 12.6 hurricanes per year. This is in sharp contrast to 2004, this being the year with the least number of hurricanes recorded, only seven, followed by the greatest number of hurricanes, 18, recorded in 2005. Another possible temporal analysis may be made by considering monthly distribution. Figure 2b shows that hurricanes in this database took place from May to December. This number gradually increased until the marked growth observed in August, with 67 hurricanes, followed by September, which had slightly fewer. A sharp decrease was noted in November, with nine hurricanes, the minimum being recorded in December with only two hurricanes. From a practical point of view, only hurricanes with the so-called GriddedData files may be useful for detailed analyses. These files are not available for the oldest hurricanes, and have only been present since 1998 for most hurricanes. However, a varying number of files may be found for each hurricane, reaching up to 60 files at different hours and days. Figure 2c presents the average number of files per hurricane. Although the mean is 9.7 and the number of files is close to this mean, this number is very noticeable in 2004, 2005, and 2008, with between 15 and 20 files per hurricane. Atmosphere 2021, 12, x FOR PEER REVIEW 4 of 13 with the least number of hurricanes recorded, only seven, followed by the greatest number of hurricanes, 18, recorded in 2005. Another possible temporal analysis may be made by considering monthly distribution. Figure 2b shows that hurricanes in this database took place from May to December. This number gradually increased until the marked growth observed in August, with 67 hurricanes, followed by September, which had slightly fewer. A sharp decrease was noted in November, with nine hurricanes, the minimum being recorded in December with only two hurricanes. From a practical point of view, only hurricanes with the so-called GriddedData files may be useful for detailed analyses. These files are not available for the oldest hurricanes, and have only been present since 1998 for most hurricanes. However, a varying number of files may be found for each hurricane, reaching up to 60 files at different hours and days. Figure 2c presents the average number of files per hurricane. Although the mean is 9.7 and the number of files is close to this mean, this number is very noticeable in 2004, 2005, and 2008, with between 15 and 20 files per hurricane. Figure 2. (a) Number of hurricanes in the HWind project during the period 1994–2013 depending on their basin. Most of them are located in the Atlantic basin. (b) Monthly distribution of hurricanes, where the highest frequencies ranged from August to October. (c) Average annual number of files per hurricane in the period 1998–2013. The years 2005, 2006, and 2008 stood out due to their noticeable values against 1998, which was the year with the lowest file number. 3.2. Analysis of Hurricane Sandy Two criteria were considered when selecting a hurricane for detailed analysis: the number of GiddedData files and the social impact. Only 24 hurricanes occurring between 2005 and 2012 were described with at least 20 GriddedData files. Of these, six reached the highest category, Category 5, and only Hurricane Katrina, in 2005, left a marked social impact. However, the current research investigates Hurricane Sandy, which occurred in 2012. Although it was only Category 3 [42], it is described by 48 GriddedData files accompanied by a noticeable social impact reflected by the extremely high number of web search Figure 2. ( a ) Number of hurricanes in the HWind project during the period 1994–2013 depending on their basin. Most of them are located in the Atlantic basin. ( b ) Monthly distribution of hurricanes, where the highest frequencies ranged from August to October. ( c ) Average annual number of files per hurricane in the period 1998–2013. The years 2005, 2006, and 2008 stood out due to their noticeable values against 1998, which was the year with the lowest file number. Atmosphere 2021,12, 1480 5 of 13 3.2. Analysis of Hurricane Sandy Two criteria were considered when selecting a hurricane for detailed analysis: the number of GiddedData files and the social impact. Only 24 hurricanes occurring between 2005 and 2012 were described with at least 20 GriddedData files. Of these, six reached the highest category, Category 5, and only Hurricane Katrina, in 2005, left a marked social impact. However, the current research investigates Hurricane Sandy, which occurred in 2012. Although it was only Category 3 [ 42 ], it is described by 48 GriddedData files accompanied by a noticeable social impact reflected by the extremely high number of web search results to emerge. The files available cover from 23 to 30 October 2012. Moreover, each file contains over 20,000 wind speed values distributed in networks centred on the hurricane between about 1000 km ×1000 km and 2000 km ×2000 km. Figure 3shows the hurricane trajectory based on the HWind files. It appeared as a tropical storm on 23 October 2012 over the Caribbean at a latitude of about 14 ◦ N. It reached Category 1 in the following 24 h and made landfall in Jamaica on 24 October 2012. The hurricane crossed the island and wind speed increased over the Cayman trough before reaching Cuba. Substantial damage was reported in Haiti. The hurricane crossed Cuba in five hours, reached Category 2 (according to these files), and lay north of the Abaco Islands on 26 October 2012, where it lost its hurricane category. However, wind speed increased and hurricane category was again reached on 27 October 2012, when it commenced a trajectory that ran parallel to the US coast for about two days. Finally, it turned west on 29 October 2012, made landfall in New Jersey as a tropical storm at a latitude of about 40◦N, and continued over the continent before disappearing. Atmosphere 2021, 12, x FOR PEER REVIEW 5 of 13 results to emerge. The files available cover from 23 to 30 October 2012. Moreover, each file contains over 20,000 wind speed values distributed in networks centred on the hurricane between about 1000 km × 1000 km and 2000 km × 2000 km. Figure 3 shows the hurricane trajectory based on the HWind files. It appeared as a tropical storm on 23 October 2012 over the Caribbean at a latitude of about 14° N. It reached Category 1 in the following 24 h and made landfall in Jamaica on 24 October 2012. The hurricane crossed the island and wind speed increased over the Cayman trough before reaching Cuba. Substantial damage was reported in Haiti. The hurricane crossed Cuba in five hours, reached Category 2 (according to these files), and lay north of the Abaco Islands on 26 October 2012, where it lost its hurricane category. However, wind speed increased and hurricane category was again reached on 27 October 2012, when it commenced a trajectory that ran parallel to the US coast for about two days. Finally, it turned west on 29 October 2012, made landfall in New Jersey as a tropical storm at a latitude of about 40° N, and continued over the continent before disappearing. Figure 3. Trajectory of Hurricane Sandy based on the HWind files together with its category. Its location at the beginning of the corresponding day is also presented. During 27 and 28 October 2012, the trajectory was parallel to the coast. However, it turned west on 29 October 2012 to reach the coast following an infrequent landfall. 3.2.1. Wind Speed Analysis The wind speed median presented in Figure 4a reveals a sharp transition on 25 October 2012, when it changed from around 9 m s−1 to nearly 16 m s−1. Moreover, a marked drop in wind speed was observed on late 27 and early 28 October 2012. However, the maximum wind speed remained above 30 m s−1 most of the time. The interquartile range presented a very soft lineal evolution from 24 October 2012 at around 5 m s−1, to 29 October 2012 with around 8 m s−1, seen in Figure 4b. The correlation coefficient of this fit is statistically significant at a 0.1% level. In a similar period, the Yule–Kendall index evolved linearly from positive skewness, around 0.4, to nearly symmetrical or even slightly leftFigure 3. Trajectory of Hurricane Sandy based on the HWind files together with its category. Its location at the beginning of the corresponding day is also presented. During 27 and 28 October 2012, the trajectory was parallel to the coast. However, it turned west on 29 October 2012 to reach the coast following an infrequent landfall. Atmosphere 2021,12, 1480 6 of 13 3.2.1. Wind Speed Analysis The wind speed median presented in Figure 4a reveals a sharp transition on 25 October 2012, when it changed from around 9 m s −1 to nearly 16 m s −1 . Moreover, a marked drop in wind speed was observed on late 27 and early 28 October 2012. However, the maximum wind speed remained above 30 m s −1 most of the time. The interquartile range presented a very soft lineal evolution from 24 October 2012 at around 5 m s −1 , to 29 October 2012 with around 8 m s −1 , seen in Figure 4b. The correlation coefficient of this fit is statistically significant at a 0.1% level. In a similar period, the Yule–Kendall index evolved linearly from positive skewness, around 0.4, to nearly symmetrical or even slightly left-skewed distributions, seen in Figure 4c. The correlation coefficient is also statistically significant at a 0.1% level for this variable. Finally, the robust kurtosis was similar to that of a Gaussian distribution, seen in Figure 4d. Atmosphere 2021, 12, x FOR PEER REVIEW 6 of 13 skewed distributions, seen in Figure 4c. The correlation coefficient is also statistically significant at a 0.1% level for this variable. Finally, the robust kurtosis was similar to that of a Gaussian distribution, seen in Figure 4d. Figure 4. (a) Median wind speed, where the sharp transition on 25 October 2012 was the most noticeable feature. (b) Interquartile wind speed range, showing a steady increase from 24 to 29 October 2012. (c) Yule–Kendall index of wind speed with a sharp dispersion of values and a decrease from slightly right-skewed to slightly left-skewed distributions. (d) Robust kurtosis of wind speed, where the dispersion of values increased with time (intercepts of linear fits were considered in the first file, on 23 October 2012 at 13.30 UTC, and slopes display the rate of change per day). Figure 5a shows an example of the wind speed histogram. Its shape describes extremely high frequencies in few central wind speed values bounded by low frequencies in the remaining wind speeds, with decreasing frequencies when the wind speed moves away from the central values. This shape suggests that the wind speed is similar in most of the region covered by the hurricane, and the Laplace distribution may suitably describe wind speed. One parameter of this distribution is the median wind speed, whose evolution was previously presented. The other parameter is the scale parameter, which may be calculated with Equation (4). Figure 5b shows its progression, where a slight linear trend with a rate of around 0.21 m s −1 each day was observed from 24 to 29 October 2012, revealing that the interval of frequent wind speeds grew wider over time, in agreement with the interquartile range. In any case, progression is somewhat irregular, with certain abrupt changes. However, the correlation coefficient is statistically significant at a 0.1% level. Figure 4. ( a ) Median wind speed, where the sharp transition on 25 October 2012 was the most noticeable feature. ( b ) Interquartile wind speed range, showing a steady increase from 24 to 29 October 2012. ( c ) Yule–Kendall index of wind speed with a sharp dispersion of values and a decrease from slightly right-skewed to slightly left-skewed distributions. ( d ) Robust kurtosis of wind speed, where the dispersion of values increased with time (intercepts of linear fits were considered in the first file, on 23 October 2012 at 13.30 UTC, and slopes display the rate of change per day). Atmosphere 2021,12, 1480 7 of 13 Figure 5a shows an example of the wind speed histogram. Its shape describes extremely high frequencies in few central wind speed values bounded by low frequencies in the remaining wind speeds, with decreasing frequencies when the wind speed moves away from the central values. This shape suggests that the wind speed is similar in most of the region covered by the hurricane, and the Laplace distribution may suitably describe wind speed. One parameter of this distribution is the median wind speed, whose evolution was previously presented. The other parameter is the scale parameter, which may be calculated with Equation (4). Figure 5b shows its progression, where a slight linear trend with a rate of around 0.21 m s −1 each day was observed from 24 to 29 October 2012, revealing that the interval of frequent wind speeds grew wider over time, in agreement with the interquartile range. In any case, progression is somewhat irregular, with certain abrupt changes. However, the correlation coefficient is statistically significant at a 0.1% level. Atmosphere 2021, 12, x FOR PEER REVIEW 7 of 13 Figure 5. (a) Wind speed histogram for 27 October 2012 at 13.30 UTC fitted to the Laplace distribution showing the noticeable values associated with the intermediate wind speeds. (b) Evolution of the scale parameter of the Laplace distribution, which presents some oscillations around the trend line. 3.2.2. Surface Analysis Isotachs were calculated each twelve hours. By way of an example, Figure 6a shows the wind speed on 27 October 2012 at 1.30 UTC. From plots such as this, isotachs corresponding to the boundaries of the Saffir-Simpson scale were selected, and the surface where the hurricane reaches each category was calculated. Moreover, since the shape of the hurricane resembles a circle, the radius corresponding to the surface equal to, or higher than, a tropical storm was calculated and is presented in Figure 6b. This radius increases linearly at a rate of around 86 km per day, with a correlation coefficient that is statistically significant at a 0.1% level. Figure 6. (a) Isotachs for 27 October 2012 at 1.30 UTC revealing the circular shape of some of them. (b) Evolution of the hurricane’s radius, assuming a circular shape for wind speed equal to, or higher than, that of a tropical storm. The linear increase was noticeable until 29 October 2012. Figure 5. ( a ) Wind speed histogram for 27 October 2012 at 13.30 UTC fitted to the Laplace distribution showing the noticeable values associated with the intermediate wind speeds. ( b ) Evolution of the scale parameter of the Laplace distribution, which presents some oscillations around the trend line. 3.2.2. Surface Analysis Isotachs were calculated each twelve hours. By way of an example, Figure 6a shows the wind speed on 27 October 2012 at 1.30 UTC. From plots such as this, isotachs corresponding to the boundaries of the Saffir-Simpson scale were selected, and the surface where the hurricane reaches each category was calculated. Moreover, since the shape of the hurricane resembles a circle, the radius corresponding to the surface equal to, or higher than, a tropical storm was calculated and is presented in Figure 6b. This radius increases linearly at a rate of around 86 km per day, with a correlation coefficient that is statistically significant at a 0.1% level. Atmosphere 2021,12, 1480 8 of 13 Atmosphere 2021, 12, x FOR PEER REVIEW 7 of 13 Figure 5. (a) Wind speed histogram for 27 October 2012 at 13.30 UTC fitted to the Laplace distribution showing the noticeable values associated with the intermediate wind speeds. (b) Evolution of the scale parameter of the Laplace distribution, which presents some oscillations around the trend line. 3.2.2. Surface Analysis Isotachs were calculated each twelve hours. By way of an example, Figure 6a shows the wind speed on 27 October 2012 at 1.30 UTC. From plots such as this, isotachs corresponding to the boundaries of the Saffir-Simpson scale were selected, and the surface where the hurricane reaches each category was calculated. Moreover, since the shape of the hurricane resembles a circle, the radius corresponding to the surface equal to, or higher than, a tropical storm was calculated and is presented in Figure 6b. This radius increases linearly at a rate of around 86 km per day, with a correlation coefficient that is statistically significant at a 0.1% level. Figure 6. (a) Isotachs for 27 October 2012 at 1.30 UTC revealing the circular shape of some of them. (b) Evolution of the hurricane’s radius, assuming a circular shape for wind speed equal to, or higher than, that of a tropical storm. The linear increase was noticeable until 29 October 2012. Figure 6. ( a ) Isotachs for 27 October 2012 at 1.30 UTC revealing the circular shape of some of them. ( b ) Evolution of the hurricane’s radius, assuming a circular shape for wind speed equal to, or higher than, that of a tropical storm. The linear increase was noticeable until 29 October 2012. 3.2.3. Recirculation Factor Analysis Figure 7a presents the air parcel trajectories ending at the hurricane centre at 10, 1000, and 5000 m in height on 27 October 2012 at 13.30 GMT. Although recirculation is noticeable for these trajectories, the main difference is that trajectories at 10 and 1000 m are simpler, like spirals, than the 5000 m trajectory, which presents loops. This behaviour may be due to surface friction, which is more accentuated near the surface, causing lower wind speeds than those recorded in the mid troposphere. These high wind speeds and the composition of rotation and translation would be responsible for complex trajectories observed at this level. Moreover, Figure 7b,c presents the evolution of the recirculation factor in the whole troposphere, calculated from trajectories obtained with the METEX model, ending at the hurricane’s centre at selected times. From a practical point of view, the layer below 1000 m is the most interesting due to its impact on human life. The recirculation factor is relatively uniform in this layer and its values are relatively high (around 0.6) most of the time. In order to investigate the influence of the end point of the air parcel trajectories on the recirculation factor, these factors were also calculated for trajectories ending at a point whose latitude was 2 ◦ lower than the hurricane’s centre latitude, but with the same longitude. Although the resulting recirculation factors varied enormously, they were, on average, around 0.1 lower for these latter trajectories in the low atmosphere, from 10 to 500 m. Atmosphere 2021,12, 1480 9 of 13 Atmosphere 2021, 12, x FOR PEER REVIEW 8 of 13 3.2.3. Recirculation Factor Analysis Figure 7a presents the air parcel trajectories ending at the hurricane centre at 10, 1000, and 5000 m in height on 27 October 2012 at 13.30 GMT. Although recirculation is noticeable for these trajectories, the main difference is that trajectories at 10 and 1000 m are simpler, like spirals, than the 5000 m trajectory, which presents loops. This behaviour may be due to surface friction, which is more accentuated near the surface, causing lower wind speeds than those recorded in the mid troposphere. These high wind speeds and the composition of rotation and translation would be responsible for complex trajectories observed at this level. Moreover, Figure 7b,c presents the evolution of the recirculation factor in the whole troposphere, calculated from trajectories obtained with the METEX model, ending at the hurricane’s centre at selected times. From a practical point of view, the layer below 1000 m is the most interesting due to its impact on human life. The recirculation factor is relatively uniform in this layer and its values are relatively high (around 0.6) most of the time. In order to investigate the influence of the end point of the air parcel trajectories on the recirculation factor, these factors were also calculated for trajectories ending at a point whose latitude was 2° lower than the hurricane’s centre latitude, but with the same longitude. Although the resulting recirculation factors varied enormously, they were, on average, around 0.1 lower for these latter trajectories in the low atmosphere, from 10 to 500 m. Figure 7. ( a ) One-day backward air parcel trajectories calculated for selected heights on 27 October 2012 at 13.30 UTC. Trajectories are spirals near the ground. However, loops are obtained in the mid troposphere. ( b , c ) Profiles of the recirculation factor at selected dates (at 13.30 UTC, except on 30 October 2012, which is at 7.30 UTC). Nearly uniform factors are observed in the low atmosphere. 4. Discussion 4.1. Database Analysis Chavas et al. [ 43 ] presented the spatial distribution of hurricane tracks on the Earth in the period 1999–2009 where the lowest number was observed over the Southern Pacific Ocean and Southern Indian Ocean. In the remaining basins, these trajectories were similar for the Atlantic and East Pacific basins. In both regions, hurricanes approached the continent from low latitudes, then veered and moved away from the continent to higher latitudes, with the greatest latitudes being reached in the Atlantic basin. However, hurricanes in the West Pacific basin were confined to low latitudes. Delgado et al. [ 44 ] reanalysed the North Atlantic hurricane database for the period 1954 to 1963. They obtained an average of around 11 storms (tropical storms and hurricanes) per year, with the number varying between 7 and 16. This average was around six for hurricanes each year, ranging between three and nine, and around three per year for major hurricanes, ranging between none and five. Most hurricanes described in Section 3.1 occur in the second part of the year. This result is in agreement with the study presented by Corporal-Lodangco and Leslie [ 45 ],