Storm Active: October 21-
Around October 13, a tropical wave began its passage across the tropical Atlantic. The system moved quite quickly westward and reached the Windward Islands on October 19.  The vigorous disturbance produced widespread heavy rainfall during its passage into the eastern Caribbean, but its high forward speed prevented a closed circulation from forming.  A little farther west, the system's forward speed slowed abruptly and it was able to become more organized.  It was named Tropical Storm Melissa during the morning of October 21.
Melissa's evolution was difficult to forecast.  On the one hand, the cyclone sat over a deep area of very warm water and had plenty of moisture to work with in the atmosphere.  On the other, it was constantly beset by strong shear out of the west.  As a result, Melissa continually developed areas of extremely strong thunderstorms which were consistently displaced east of the center.  Oftentimes the low-level circulation of Melissa outpaced the convective mass, but this swirl would dissipate as the center reformed farther east.  At the same time, due to Melissa being wedged between two mid-level ridges, steering currents were very weak and the cyclone did little more than meander for days.  Overall it made a little progress north and west between its naming and October 24.  Though the system remained away from land, rain on the outskirts of the storm caused torrential rains over portions of Hispaniola.
Around that time, though, wind shear began to gradually diminish and the system's structure changed.  Organized outer bands developed and a central dense overcast appeared on the 25th.  After these elements were in place, rapid intensification began.  Melissa reached hurricane strength that afternoon and major hurricane strength just 9 hours afterward.  By that time, an eye began to clear out. On October 26, the storm briefly paused deepening at category 4.  Meanwhile, it had assumed a slow westward track, pushed by a weak mid-level ridge to the north.  It tracked south of Jamaica and tropical storm conditions occurred along the southern coast of the island in outer bands.
Early on October 27, Melissa's satellite presentation became even more symmetric and the area of extremely intense thunderstorms around the eyewall grew, extending even higher into the atmosphere.  This prompted an upgrade to category 5 intensity.  Melissa was the third category 5 of the season after Erin and Humberto.  This made 2025 only the second season on record with three or more category 5 hurricanes, after 2005, which featured four.
Over the next day, an approaching trough over eastern North America eroded the ridge that was steering Melissa and began to pull the cyclone, causing it to turn toward the north-northeast.  This set it on a path toward Jamaica.  It was, meanwhile, moving over some of the highest ocean heat content waters in the world.  Though already a category 5, Melissa continued strengthening, avoiding the usual fluctuations in intensity that arise from eyewall replacement cycles common to powerful cyclones.  During the morning of October 28, a few hours before Melissa's center made landfall in western Jamaica, the hurricane reached its extreme peak intensity.  At its peak, the storm had estimated sustained winds of 185 mph and a minimum central pressure of 892 mb.  It made landfall at this peak soon after.
Melissa's strength set a number of records.  The 892 mb mark tied the Labor Day Hurricane of 1935 for most intense at landfall by minimum pressure in a recorded Atlantic huricane.  This same pressure mark tied for third lowest ever recorded in an Atlantic hurricane, behind only Gilbert of 1988 and Wilma of 2005.  The winds of 185 mph tied with several other hurricanes for second highest recorded in the Atlantic, behind only Allen of 1980.  The wind damage wrought by the storm was catastrophic in western Jamiaca where the center passed through.  The mountainous terrain did disupt Melissa enough to weaken it to a category 3 hurricane by the time it emerged back over water early that evening.
The storm had a brief resurgence in strength late on the 28th as a large eye redeveloped on satellite, and it was upgraded back to a category 4.  Soon after that, though, wind shear out of the southwest began to disrupt Melissa's core again, and it weakened back to a category 3 at landfall in eastern Cuba in the early morning hours of October 29.  The system continually accelerated northeastward, crossing quickly into the Atlantic and passing among the southeastern Bahamas as a category 1 that afternoon.  Despite some shear, it managed to intensify slightly again over the western Atlantic to category 2 strength.  The remaining core convection became displaced from the center on October 30, but Melissa was still a formidable cyclone as it rocketed by just west of Bermuda that evening.
As of 8:00pm on October 30, 2025, Hurricane Melissa had maximum sustained winds of 105 mph, a minimum central pressure of 970 mb, and was moving northeast at 32 mph.  For more up-to-date information and the latest watches and warnings, please consult the National Hurricane Center.
Tuesday, October 21, 2025
Saturday, October 18, 2025
Two Fun Factorizations
I recently came across the following pair of numbers, quite close to one another, and with similar-looking prime factorizations:
4061 = 31*131
4069 = 13*313
We can explain the proximity of these two numbers by expanding the products as follows:
4061 = (3*10 + 1*1)(1*100 + 3*10 + 1*1) = 3*1000 + 9*100 + 1*100 + 3*10 + 3*10 + 1*1 4069 = (1*10 + 3*1)(3*100 + 1*10 + 3*1) = 3*1000 + 9*100 + 1*100 + 3*10 + 3*10 + 3*3
Notice that only the last terms are different, leading to the difference 3*3 - 1*1 = 8 between the two numbers.
The same sort of argument shows that products of the aba...ba*ba and bab...ab*ab differ only by a*a - b*b, where a and b are any two digits. However, a computer search yields no other examples where all of these numbers are prime, besides the above, up to at least a googol.
4061 = 31*131
4069 = 13*313
We can explain the proximity of these two numbers by expanding the products as follows:
4061 = (3*10 + 1*1)(1*100 + 3*10 + 1*1) = 3*1000 + 9*100 + 1*100 + 3*10 + 3*10 + 1*1 4069 = (1*10 + 3*1)(3*100 + 1*10 + 3*1) = 3*1000 + 9*100 + 1*100 + 3*10 + 3*10 + 3*3
Notice that only the last terms are different, leading to the difference 3*3 - 1*1 = 8 between the two numbers.
The same sort of argument shows that products of the aba...ba*ba and bab...ab*ab differ only by a*a - b*b, where a and b are any two digits. However, a computer search yields no other examples where all of these numbers are prime, besides the above, up to at least a googol.
Labels:
Mathematical Oddities
Monday, October 13, 2025
Tropical Storm Lorenzo (2025)
Storm Active: October 13-15
On October 10, a tropical wave entered the Atlantic from Africa. The wave was vigorous and developed fairly quickly, leading to the naming of Tropical Storm Lorenzo on October 13. At the time, it was located around 1000 miles west of Cabo Verde. This was fairly late in the season for a tropical cyclone to form in the "Main Development Region" of the tropical Atlantic between Africa and the Lesser Antilles.
Lorenzo experienced significant shear out of the southwest, preventing it from intensifying much as it moved northwestward. Even after shear lessened the next day, the storm entered an area of dry mid-level air that stifled convective developement. Without moist unstable air to drive its circulation, Lorenzo began to spin down quickly. It curved toward the north-northeast and steadily weakened before dissipating on October 15.
The image above shows Lorenzo on October 14.
Lorenzo did not affect any land areas as a tropical cyclone.
On October 10, a tropical wave entered the Atlantic from Africa. The wave was vigorous and developed fairly quickly, leading to the naming of Tropical Storm Lorenzo on October 13. At the time, it was located around 1000 miles west of Cabo Verde. This was fairly late in the season for a tropical cyclone to form in the "Main Development Region" of the tropical Atlantic between Africa and the Lesser Antilles.
Lorenzo experienced significant shear out of the southwest, preventing it from intensifying much as it moved northwestward. Even after shear lessened the next day, the storm entered an area of dry mid-level air that stifled convective developement. Without moist unstable air to drive its circulation, Lorenzo began to spin down quickly. It curved toward the north-northeast and steadily weakened before dissipating on October 15.
The image above shows Lorenzo on October 14.
Lorenzo did not affect any land areas as a tropical cyclone.
Labels:
2025 Storms
Friday, October 10, 2025
Subtropical Storm Karen (2025)
Storm Active: October 9-10
Around October 8, a non-tropical low pressure system formed well to the northwest of the Azores. The low quickly separated from the surrounding fronts and developed a tiny warm core, embedded in a larger upper-level trough. These characteristics, along with gale force winds, led to the designation of Subtropical Storm Karen late on October 9. This was the northernmost formation by an Atlantic tropical or subtropical cyclone on record, at 44.5°N.
Besides this impressive statistic, Karen did not lead a very notable existence. The small area of convection near the center was snuffed out the following afternoon when the storm moved even farther north over yet colder waters. By that evening, the system was declared post-tropical.
Karen carved out a warm core inside a larger system and managed to maintain subtropical cyclone status for a day before becoming post-tropical.
Around October 8, a non-tropical low pressure system formed well to the northwest of the Azores. The low quickly separated from the surrounding fronts and developed a tiny warm core, embedded in a larger upper-level trough. These characteristics, along with gale force winds, led to the designation of Subtropical Storm Karen late on October 9. This was the northernmost formation by an Atlantic tropical or subtropical cyclone on record, at 44.5°N.
Besides this impressive statistic, Karen did not lead a very notable existence. The small area of convection near the center was snuffed out the following afternoon when the storm moved even farther north over yet colder waters. By that evening, the system was declared post-tropical.
Karen carved out a warm core inside a larger system and managed to maintain subtropical cyclone status for a day before becoming post-tropical.
Labels:
2025 Storms
Tropical Storm Jerry (2025)
Storm Active: October 7-11
On October 3, a late season tropical wave entered the Atlantic basin. It moved quickly toward the west-northwest and steadily organized. By October 6, the wave had a very impressive satellite signature, featuring a broad area of spin and concentrated thunderstorm activity. The next day, it was named Tropical Storm Jerry. Jerry was still over a thousand miles east of the Lesser Antilles, but was moving quickly toward the west-northwest. Despite a strong start, the storm actually became less organized after it was named. By the next day, shear opposite to its forward motion had displaced all thunderstorm activity east-southeast of the center. Nevertheless, it managed to strengthen some through the evening of October 8.
Jerry approached the Leeward Islands the next day. The center made its closest approach to land during the evening of the 9th, but the accompanying rains peaked over the islands only overnight and into the next morning, since convection was so removed from the center. The storm wasn't strong, but did cause widespread flooding for the northeasternmost Caribbean islands. Only on the 10th did Jerry lift north away from the Leewards. The cyclone's center was very poorly defined, with a pronounced elongation in the northwest-southeast direction. The cyclone was never able to recover from this poor organization and lost its circulation on October 11, degenerating into a trough of low pressure.

The image above shows Jerry just east of the Leeward Islands on October 9. The center of circulation ultimately missed the islands, but Jerry's passage dragged an area of heavy rain, displaced south and east of the center, across those areas over the following day.
Jerry dissipated shortly after its brush of the Caribbean.
On October 3, a late season tropical wave entered the Atlantic basin. It moved quickly toward the west-northwest and steadily organized. By October 6, the wave had a very impressive satellite signature, featuring a broad area of spin and concentrated thunderstorm activity. The next day, it was named Tropical Storm Jerry. Jerry was still over a thousand miles east of the Lesser Antilles, but was moving quickly toward the west-northwest. Despite a strong start, the storm actually became less organized after it was named. By the next day, shear opposite to its forward motion had displaced all thunderstorm activity east-southeast of the center. Nevertheless, it managed to strengthen some through the evening of October 8.
Jerry approached the Leeward Islands the next day. The center made its closest approach to land during the evening of the 9th, but the accompanying rains peaked over the islands only overnight and into the next morning, since convection was so removed from the center. The storm wasn't strong, but did cause widespread flooding for the northeasternmost Caribbean islands. Only on the 10th did Jerry lift north away from the Leewards. The cyclone's center was very poorly defined, with a pronounced elongation in the northwest-southeast direction. The cyclone was never able to recover from this poor organization and lost its circulation on October 11, degenerating into a trough of low pressure.

The image above shows Jerry just east of the Leeward Islands on October 9. The center of circulation ultimately missed the islands, but Jerry's passage dragged an area of heavy rain, displaced south and east of the center, across those areas over the following day.
Jerry dissipated shortly after its brush of the Caribbean.
Labels:
2025 Storms
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