Pacific Spotlight: Hurricane Lala (2026)

The 2026 Atlantic hurricane season has been very quiet, due to the 2026 super El Niño event. As often happens, the opposite is true for Pacific tropical cyclone activity: all parts of the northern Pacific have been very active thus far. In this post, we'll discuss Hurricane Lala, pictured below, as well as meander through some topics related to Pacific storms, which are rarely touched on by this blog.

Lala recently claimed the interesting title of being the longest-lived tropical cyclone ever to exist entirely within the Central Pacific. This distinction is mostly an artifact of how tropical cyclones are classified: the enormous breadth of the Pacific north of the equator is divded into three areas, according to the meteorological center responsible for issuing advisories on tropical cyclones in the area.



The East Pacific extends from the coastline of the Americas to 140°W, and is administered, along with the north Atlantic, by the National Hurricane Center in Miami, Florida. Cyclones in this region are called hurricanes. The West Pacific is defined to extend from 180 (the International Dateline) to Asia, specifically the 100°E line of longitude, and is administered by the Typhoon Center in Tokyo, Japan. Cyclones in this region are called typhoons. In the middle, between 140° W and the Dateline, is the Central Pacific, administered by the Central Pacific Hurricane Center in Honolulu, Hawaii.



The images above show the headquarters of the Central Pacific Hurricane Center (CPHC), established 1970. It is located on the campus of the University of Hawaii at Manoa. I actually took these photos myself on a recent visit to the campus.

As mentioned, these boundaries are not meteorologically significant. In fact, tropical cyclones frequently cross between these regions. This creates some fun naming quirks. The terminology of "tropical storms" and "hurricanes" are used the same way in the Central Pacific as in the Eastern Pacific and Atlantic. However, a "Hurricane X" crossing the International Dateline westward changes to "Typhoon X", preserving its name but changing its title. In the tropics, most tropical cyclones move westward, so it is quite common for cyclones to cross from the Eastern to Central Pacific, and not unusual for Central Pacific cyclones in turn to cross to the West Pacific. Farther from the equator, tropical cyclones often "recurve" toward the northeast due to the midlatitude westerly winds, so occasionally a crossing happens in the other direction. A notable example is Hurricane/Typhoon John of 1994, whose track is shown below.

John formed and was named in the Eastern Pacific, crossed to the Central, passed south of Hawaii, crossed the International Dateline and was renamed "Typhoon John", and finally crossed back into the Central Pacific near the end of its long journey. John still has the longest total track of any tropical cyclone on record. Many years ago, a previous post on this blog discussed John's track in some detail, though its longevity record has since been usurped by Cyclone Freddy of the southern Indian Ocean.

Since John made three of the four possible crossings, it's natural to ask whether a cyclone has ever done the remaining one: crossing from the Central Pacific eastward into the Eastern Pacific. This is far rarer because the mid-latitude east Pacific waters are comparatively cold, and tropical cyclones usually fizzle before recurving. One notable historical example is Hurricane Ulika of 2016.

The tropical depression that became Ulika formed in the eastern Pacific in September 2016, just east of 140°W, crossed into the Central Pacific, was named there, crossed back into the Eastern Pacific, and then crossed again into the Central before losing tropical cyclone status.

Each region also uses its own naming system, and a cyclone always keeps its name from the first time it achieves tropical storm strength ("John" came from the Eastern Pacific, "Ulika" from the Central). The Atlantic and Eastern Pacific use familiar alphabetical lists of storms that begin at "A" each year, rotating in a six-year cycle. In contrast, the Central Pacific uses four lists of twleve names each, which do not reset each year but rather pick up where the last year left off. The name "Lala" was the first used in the Central Pacific in 2026, picking up from "Keli" in 2025. Just as in the other regions, the names of particularly damaging cyclones are retired. The full lists can be found here; they use traditional Hawaiian names and were selected in partnership with cultural experts. The name "Lala" means "branch" or "tree limb" in Hawaiian.

One reason for the difference in naming convention is that relatively few cyclones are named in the Central Pacific, compared to its eastern and western neighbors.



The image above shows the total number of named storms in the central Pacific for each year from 1970-2013 including storms that formed in other regions and crossed over. These numbers are already smaller than neighboring basins, and the number of names used from the Central Pacific lists per year is far smaller. This is mainly due to the low atmospheric humidity in the region and a persistent upper-level troughs of low pressure that tend to shear apart nascent storms.

The El Niño Southern Oscillation (ENSO) cycle, however, has an outsized effect on Central Pacific activity. This multi-year cycle is a trend in the temperature anomalies in the equitorial Pacific ocean; positive anomalies lead to an "El Niño" and negative ones to a "La Niña". Studies show that Central Pacific activity doubles during El Niño, compared to La Niña. This brings us at last back to 2026, as this summer has seen possibly the largest El Niño in recorded history take shape.

On August 9, 2026, a tropical wave entered the Central Pacific, moving west-northwestward. The disturbance was large but organized steadily, taking advantage of higher than normal oceanic heat content and favorable atmospheric conditions. Early in the morning on August 13, Hawaii time, it was named Tropical Storm Lala, around 700 miles (1100 km) east-southeast of the Big Island. Not all factors were in favor of intensification: Lala had some mid-level dry air to contend with, and was somewhat asymmetric, with most convection and winds north of the circulation center. Nevertheless, the storm gradually deepened, and was a strong tropical storm by late on the 14th. Early the next morning, its outer rainbands swept across the Big Island, with tropical storm force winds beginning shortly thereafter. Lala strengthened some more during its final approach to the Big Island, and peaked as a category 1 hurricane with maximum sustained winds of 80 mph (130 km/hr) and a central pressure of 985 mb as the center passed within 30 miles (50 km) of the southernmost point of Hawaii around 5pm local time.

The image above shows Lala at its first peak as it passed close to the Big Island. As discussed further below, the size of the storm meant that significant storm impacts were felt across the Hawaiian islands, even though the hurricane did not technically make landfall. After its close passage, dry air flowing off the mountains of Hawaii temporarily weakened the storm, bringing it down to tropical storm status. Lala turned westward away from the island chain, and most impacts even to the westernmost main Hawaiian islands had ended by late on August 16.

Lala had limited atmospheric moisture to work with and was battling some shear, but the increasingly warm waters it traversed were enough to begin another strengthening trend the next day. The storm put on an impressive display and made it all the way to category 4 intensity late on August 18. The peak intensity was 130 mph (210 km/hr) winds with a central pressure of 947 mb. The image at the beginning of this post shows Lala around that peak.

Meanwhile, the storm was turning toward the right as the ridge north of it weakened. The rest of Lala's history was mostly a slow weakening trend. It passed over the uninhabited northwestern Hawaiian islands and atolls still as a category 1 hurricane on August 20. After a slight resurgence to category 2, Lala resumed weakening as it encountered steadily cooler waters in the subtropics. It did not accelerate northeastward, though, but instead resumed a plodding northwest trajectory as another ridge blocked its exit. The storm spent another week on this general path, diminishing to a tropical storm on August 22 and finally to a post-tropical storm on August 27, just east of the International Dateline, having reached a latitude over 38°N.

Lala spent 14.5 days as a tropical cyclone, all in the Central Pacific. This surpassed the previous Central Pacific record of Hurricane Ana of 2014, which had lasted 12.75 days. Notably, the storm took a jog near the islands: it approached on a west-northwest path, turned a little left and avoided a Big Island landfall, and then curved back to the right after passing the Big Island before resuming a westward course. This is actually a well-studied phenomenon; data indicate that the high topography of the Big Island influences the track of approaching storms, deflecting them in a curve around land.



Still, such events are not so common. The image above shows tropical cyclones of tropical storm strength or above that have passed within 50 miles of Hawaii in the period 1949-2026. Lala is the closest hurricane approach to the Big Island in the official record, though historical accounts suggest a significant hurricane may have made landfall there in 1871. The category 4 landfall of Hurricane Iniki in Kauai on September 11, 1992 remains the strongest ever recorded in the state.



Regardless of the specifics of how close Lala came to landfall, its effects were widespread. The map above shows the total rainfall map over the duration of the storm. As always in Hawaii's climate, the mountains had a huge impact: east-facing mountainsides and coastlines faced the oncoming winds as the counterclockwise rotation of Lala brought rainbands into the islands from the sea. These areas received extreme rain totals, in contrast to smaller amounts in the leeward areas. The greatest total was 43.54 inches of rain (1106 mm) at Laupāhoehoe, a point in the northeast corner of the Big Island. This was the third-largest rainfall total ever recorded in the state of Hawaii from a tropical cyclone. These rains caused widespread flooding. Footage from the summit of Mauna Kea also recorded snowfall as the storm passed, a very rare effect for a hurricane. Widespread tropical storm force winds also occurred across the islands, with peak gusts on the Big Island, Maui, and Oahu reaching hurricane strength. These winds knocked out power for hundreds of thousands of people. The highest recorded gust, again at the Mauna Kea summit, was a remarkable 140 mph (225 km/hr).

Hawaii continues to recover from Lala's passage. There were 3 known direct fatalities from the hurricane. The storm's approach was well-predicted, however, with a close pass anticipated before Lala was even named. These improvements in forecasting are essential to hurricane safety preparations.

The continuing El Niño event will likely bring other tropical cyclones to the region near Hawaii in the coming year. For now, Lala is the latest chapter in the not-so-well-known story of Central Pacific hurricanes.

Sources:

• https://community.wmo.int/site/knowledge-hub/programmes-and-initiatives/tropical-cyclone-programme-tcp/tropical-cyclone-regional-bodies,
• https://www.nhc.noaa.gov/aboutcphc.php, https://www.hawaiinewsnow.com/2026/08/23/lala-moke-how-hawaiis-tropical-storms-get-their-unique-names/,
• https://www.nytimes.com/2026/08/15/weather/tropical-storm-lala-name-hawaii-hurricane.html,
• https://yaleclimateconnections.org/2026/08/hawaii-reeling-after-lalas-powerful-sideswipe/
• "North-Central Pacific Tropical Cyclones: Impacts of El Nin˜o–Southern Oscillation and the Madden–Julian Oscillation" by Klotzbach and Blake, 2013
• "The Effect of Hawai’i’s Big Island on Track and Structure of Tropical Cyclones Passing to the South and West" by Chambers and Li, 2011

Tropical Storm Dolly (2026)

Storm Active: August 27-28

On August 24, a tropical wave moved off the coast of Africa and began a crossing of the tropical Atlantic. Conditions were marginally favorable for developement; the system managed to organized and become a small tropical storm on August 27, earning the name Dolly. Dolly was moving very quickly westward, and faced high wind shear as it approached the Caribbean; such conditions had dominated the Caribbean most of hurricane season up to that point. The storm's forward speed of nearly 25 mph in high shear made it very difficult to maintain a closed vortex. Late morning on the 28th, satellite observations indicated that Dolly had opened up into a tropical wave and dissipated.

Even though the system no longer had a closed circulation, it still continued to bring an area of showers and thunderstorms westward. By late on August 29, these rains reached the northeastern Caribbean.

Tropical Storm Cristobal (2026)

Storm Active: August 12-13

On August 11, an area of low pressure formed over the subtropical Atlantic, northeast of Bermuda. It developed a well-defined circulation as it moved steadily eastward, but at first did not have enough convective activity to be classified a tropical cyclone. The next day, however, it found a window of favorable conditions which allowed it to be named Tropical Storm Cristobal. The new tropical storm's tenure was very short-lived, however, for its eastward path brought it over cooler waters. In addition, strong upper-level winds stripped the cyclone from the northwest. This combination of factors weakened Cristobal to a tropical depression and then a remnant low on August 13.

Tropical Storm Cristobal was beset by unfavorable conditions immediately after being named.

Cristobal spent only around one day as a tropical cyclone.

Tropical Storm Bertha (2026)

Storm Active: July 19-23

Around July 17, a low pressure system formed in the northeastern Gulf of Mexico. The disturbance was associated with a broad area of showers and thunderstorms extending over Florida and the waters to the east. The broad system gradually organized and moved very slowly northwestward. On July 19, the circulation was well-defined enough to be designated Tropical Depression Two. Dry air from the mainland U.S. was impinging on the center from the north, limiting convection and slowing strengthening. As a result, it took until the evening of July 20 for the storm to intensify into Tropical Storm Bertha.

A strong ridge over land kept Bertha from gaining much latitude, and it instead turned slowly westward. The storm did deepen some, but most storms remained on the southern side off of land, even though the center was less than 100 km from land. Unusually, this resulted in the main land impact along the Gulf coast being gale force winds. Land interaction and dry air capped Bertha at a moderately strong tropical storm and began to weaken the system on July 21. The next day, it crossed westward over southeastern Louisiana. Bertha briefly emerged over water after that encounter and so managed to maintain tropical storm strength a little longer. On the 23rd, though, it made its final landfall near the Louisiana/Texas border. Once inland over Texas, the system degraded more quickly and dissipated entirely that night.

The image above shows Bertha near peak intensity on July 21. Most cloud cover is displaced south of the center of circulation.

Bertha took a somewhat unusual westward track across the Gulf of Mexico.

Tropical Storm Arthur (2026)

Storm Active: June 17

During the second week of June, a tropical wave crossed the Caribbean sea and moved over the Yucatan peninsula. On June 12, a low pressure area formed at the end of the wave in the Bay of Campeche. Two days after that, the low moved inland over northeastern Mexico, which halted tropical development. The low moved generally northward and crossed over Texas before drifting back toward the Gulf of Mexico, into which it emerged on the 16th. The disturbance organized into Tropical Storm Arthur a day later. The disorganized system moved northeastward parallel to the Texas coastline, accelerating as it did so, until it made landfall late that evening. It lost tropical cyclone status very soon after.

Though Arthur was short-lived, it and its remnants brought significant rainfall to the Gulf coast and later to the southeastern United States as it moved across the country.

Arthur was quite a disorganized storm, with its center displaced from the heaviest thunderstorm activity.

Arthur only briefly held tropical storm status over the Gulf of Mexico before moving back over land.

Professor Quibb's Picks – 2026

My personal prediction for the 2026 North Atlantic Hurricane season (written June 1, 2026) is as follows:

11 cyclones attaining tropical depression status,
10 cyclones attaining tropical storm status,
5 cyclones attaining hurricane status, and
2 cyclones attaining major hurricane status.

These predictions are below the 1991-2020 averages of 14.4 tropical storms, 7.2 hurricanes, and 3.2 major hurricanes each season. The forecast this year is dominated by the expectation of a strong El Niño event. An El Niño is characterized by a positive sea surface temperature anomaly in the Pacific Ocean near the equator. This phenomenon has a name due to its significant correlation with weather patterns around the globe, including tropical cyclone activity. Past El Niño events have corresponded to less active Atlantic hurricane seasons. The signal for a developing El Niño this year is already quite strong:

The chart above shows SST anomalies in four different parts of the equatorial Pacific over the last year. After a string of moderately negative anomalies in the winter, temperatures have rapidly increased over the last couple of months. Models indicate that this increase should continue into the autumn:

The bars indicate the probabilities of various strength El Niño events for upcoming three-month periods, initialized in May 2026. It's quite plausible that composite anomalies will exceed 2 degrees Celsius late in the Fall. Even if they don't reach this mark, it is quite likely that this will be the strongest El Niño in over a decade, since the fall and winter of 2015-2016. All this should add up to a significant suppressing effect on cyclone acitivity.

Moving on to a couple other indicators, we can look at something closer to home: ocean temperatures in the Atlantic itself.

Climate models for the summer indicate a somewhat warm Atlantic relative to the 1984-2009 baseline, as one would expect from a warming climate in any case. Variations from the recent year-to-year average are not especially noteworthy in any part of the basin, though, so this factor is more-or-less a wash. Finally, we'll examine what's expected for the upper atmosphere:

The figure above shows simulated data for the coming August, specifically zonal wind anomalies at the 250mb level of the atmosphere, which is roughly 34,000 feet (or a little over 10km) in height. "Zonal" wind refers to the component of wind in the east-west direction, and the dominant red color indicates higher than normal such winds. Usually, strong horizontal winds in the upper atmosphere mean that the difference in the wind vector between the lower and upper atmosphere (wind shear) is more pronounced. This in turn is disruptive to forming cyclones because it makes it harder for a vortex to "stack" vertically. This is an expected byproduct of an El Niño event, but the effect is notably strong.

All this put together suggests a below average hurricane season. My forecast of 10 named storms would be the lowest since the 2014 season. Next, I'll give a finer analysis of the risks by region. My estimates are on a scale from 1 (least risk) to 5 (most risk).

U.S. East Coast and Atlantic Canada: 2
During an El Niño season, the persistent Bermuda-Azores high pressure system over the subtropical eastern Atlantic is typically weaker than normal, giving the hurricanes that do develop an "escape hatch" out to sea before they reach land. Combined with the smaller than expected number of storms overall, this should decrease the risk to the eastern seaboard this season.

Yucatan Peninsula and Central America: 2
The southwest Caribbean should be fairly warm, and carries the potential for some systems to develop and immediately effect nearby landmasses. However, an unfavorable atmosphere will likely curb cyclone development, and the fact that the Pacific hurricane season is likely to be active means that Pacific storms might interfere with the spinning up of Atlantic ones.

Carribean Islands: 2
El Niño events are usually warm and dry in the Caribbean, and wind shear will be an obstacle to hurricanes reaching the islands intact. Nevertheless, I expect a few struggling storms to make it to the eastern islands, with the potential for a stronger one to sneak through before going out to sea if shear temporarily relaxes.

Gulf of Mexico: 1
The Gulf should be quiet this year. Most storms will curve east rather than taking the traditional west-northwest track. Further, some of the highest expected zonal wind anomalies are over the Gulf region. I expect an early end to hurricane season in this region.

Overall, I expect the 2026 Atlantic hurricane season to be below average. Nevertheless, this is just an amateur forecast. Individuals in hurricane-prone areas should always have emergency measures in place. For more on hurricane safety sources, see here. Remember, devastating storms can occur even in otherwise quiet seasons.

Sources: https://storymaps.arcgis.com/stories/644d2a771dff44fb826a2ee4f9c5b936, https://www.cpc.ncep.noaa.gov/products/analysis_monitoring/lanina/enso_evolution-status-fcsts-web.pdf, https://www.tropicaltidbits.com/analysis/models/, https://yaleclimateconnections.org/2026/05/whats-a-super-el-nino-and-other-el-nino-questions-answered/

Hurricane Names List – 2026

The name list for tropical cyclones forming in the North Atlantic basin for the year 2026 is as follows:

Arthur
Bertha
Cristobal
Dolly
Edouard
Fay
Gonzalo
Hanna
Isaias
Josephine
Kyle
Leah
Marco
Nana
Omar
Paulette
Rene
Sally
Teddy
Vicky
Wilfred

This list is the same as that for the 2020 season, with the exception of Leah, which replaced the retired name Laura.

2025 Season Summary

The 2025 Atlantic hurricane season was near average in activity, with a total of

13 cyclones attaining tropical depression status,
13 cyclones attaining tropical storm status,
5 cyclones attaining hurricane status, and
4 cyclones attaining major hurricane status.

Before the beginning of the season, I predicted that there would be

15 cyclones attaining tropical depression status,
13 cyclones attaining tropical storm status,
6 cyclones attaining hurricane status, and
3 cyclones attaining major hurricane status.

The average numbers of tropical storms, hurricanes and major hurricanes (over the 30 year period 1991-2020) per season are 14.4, 7.2, and 3.2, respectively. My forecasted numbers were close to the final outcome in all categories. This season fell just below average in number of tropical storms and hurricanes, but notably had several very intense hurricanes, including three category 5's. The (preliminary) total Accumulated Cyclone Energy for the 2025 season is 132.6 units, which modestly exceeded the 30-year climatological average of 122.5.

The near-average total activity during the 2025 season is consistent with the mixed bag of atmospheric and oceanic indicators discussed in the pre-season summary. As forecast, ENSO neutral conditions prevailed through the entire hurricane season, with neither an El Niño nor a La Niña event active to suppress or enhance cyclone activity. As in the previous few years, Atlantic sea temperatures were well above the 30-year average, though the anomalies did not match the extreme ones of 2023 and 2024. The impact of these high ocean temperatures mainly lay in boosting hurricanes' intensity: despite having relatively few cyclones, 2025 featured a remarkable three category 5 hurricanes: Erin, Humberto, and Melissa. This was only the second time in recorded history that the Atlantic saw more than two category 5 hurricanes, after 2005 (which had 4).

Erin and Humberto reached category 5 strength over the western tropical Atlantic, an unusual feat made possible by ocean heat content reaching values usually only seen in the Gulf of Mexico or Caribbean. Finally, exceptionally warm waters in the western Caribbean allowed Melissa to become one of the strongest tropical cyclones ever recorded, reaching peak sustained winds of 190 mph winds and a minimum pressure of 892 mb on October 28. In terms of pressure, Melissa tied for third most intense among recorded Atlantic hurricanes, and was the strongest storm globally in 2025. Melissa tied Hurricane Allen of 1980 for the strongest sustained winds ever recorded in an Atlantic hurricane. Its landfall in Jamaica at 897 mb was the second lowest ever for a landfalling hurricane, behind only the 1935 Labor Day Hurricane in the Florida Keys.

The map above shows all tropical cyclone tracks for 2025. It's notable that, with the glaring exception of Melissa, the south and west areas of the Atlantic basin were very quiet. In particular, the continental U.S. and Mexico each had only one Atlantic tropical storm make landfall. My area-specific forecast underestimated the risk to the Caribbean islands, and overestimated it elsewhere. The fortunate fact that most hurricanes went out to sea can be chalked up in part to a persistent pattern of upper-level troughing near the U.S. southeast.

The map above illustrates the upper-atmospheric pattern during peak hurricane season (August-October), highlighting lower than normal pressures over the U.S. southeast. This pattern generated flow from the southwest pushing hurricanes northeast out to sea, away from major landmasses.

A strange feature of the 2025 season that was repeated from 2024 was a lull in activity right at the climatological peak of hurricane season! This year, no named storms formed between August 24 and September 16 (compare to last year's lull between August 13 and September 9, which was even starker compared to the overall busy season). The last time no named storms formed in this date range is 1992, and before that 1939. A combination of features was responsible, including a regime of high sea-level pressure over the subtropical Atlantic (see below).

The map above shows a consistent high pressure area over the subtropics (red) in late August through mid-September. In the northern hemisphere, air flows clockwise around such high pressure areas, so cool and dry air from the northeast Atlantic was pushed down into the tropics, stifling the development of tropical waves coming off of Africa. Coupled with a high shear environment in the Caribbean during these dates, this effectively shut down hurricane activity.

Some other notable facts and figures from 2025 include:

• Tropical Storm Barry's remnants contributed to a devastating flash flood event in Texas on July 4-5 several days after its dissipation
• Hurricane Erin tied for the third-largest 24-hour pressure drop recorded in an Atlantic hurricane, dropping 83 mb from 998 mb to 915 mb on August 15-16 (the number one spot still belongs to 2005's Hurricane Wilma, the strongest Atlantic hurricane on record)
• Hurricanes Humberto and Imelda came close enough together to undergo a binary interaction, which altered the course of each hurricane (see the satellite image below); in fact, the minimum distance between the centers of the cyclones on September 30, around 466 miles (405 nautical miles, 750 kilometers), was the smallest recorded between two Atlantic hurricanes during the satellite era
• Subtropical Storm Karen was named at 44.5°N, the farthest north any Atlantic cyclone had been named
• A dropsonde instrument dropped from reconaissance aircraft measured a wind gust of 252 mph in the eyewall of Melissa a few thousand feet above sea level. This was later confirmed to be the strongest gust ever directly measured in a tropical cyclone on Earth.

The satellite image above shows the interaction between Humberto and Imelda, which had the fortunate consequence of pulling Imelda eastward out to sea before it could make landfall in the U.S.

Overall, the 2025 Atlantic hurricane season had total statistics near the recent average, hiding the fact that it also had several exceptionally strong hurricanes.

Sources: "ENSO: Recent Evolution, Current Status and Predictions" from the Climate Prediction Center, CSU Department of Atmospheric Science Real-time Tropical Cyclone Activity, CSU Summary of 2025 Tropical Cyclone Activity, "2025 Atlantic hurricane season marked by striking contrasts" from the NOAA, Yale Climate Connections: "A Cat 4 and 5 extravaganza: A look back at the 2025 Atlantic hurricane season", Hurricane Humberto Tropical Cyclone Report (NOAA),

Squares with Ascending Digits

Yesterday's date, November 22, 2025, prompted me to think about square numbers with ascending digits (in base 10). In the month-day-year abbreviation, the digits of yesterday's date form 112225, which is a square number! In particular, 112225 = 335². Interestingly, both 335 and 112225 have an ascending digit sequence. It turns out that such squares, while rare, occur infinitely often. 112225 is a member of one of several similar infinite sequences. This one begins:

25, 1225, 112225, 11122225,...

Here the nth entry of the sequence has n-1 1's, followed by n 2's, and then a single 5 at the end. These are the squares of the sequence:

5,35,335,3335,....

Let's prove this fact by induction. Clearly, it is true that 5² = 25. Assume the nth term of the bottom sequence, a_n squares to the nth of the top sequence, b_n. Then we notice:

a_n+1 = 3*10ⁿ + a_n

so that

a_n+1² = (3*10ⁿ + a_n)² = 9*10²ⁿ + 6*10ⁿ*a_n + a_n². Now the key point is that 3*a_n is just 6 more than 333...33*3 = 999...99, so that 3*a_n = 10...05 = 10ⁿ + 5, and hence 6*a_n = 20...010 = 2*10ⁿ + 10. Simplifying the above equation then gives

a_n+1² = 9*10²ⁿ + 2*10²ⁿ + 10ⁿ⁺¹ + a_n² = 1*10²ⁿ⁺¹ + 1*10²ⁿ + 1*10ⁿ⁺¹ + a_n².

Finally, we see that to get from a_n² = b_n to a_n+1², we add two 1's to the very beginning of the number (1*10²ⁿ⁺¹ + 1*10²ⁿ) and then change the final 1 in the sequence of 1's to a 2, by adding 1*10ⁿ⁺¹. This results in precisely b_n+1, as claimed.

It'd be interesting to see whether there are higher perfect powers with ascending digit sequences; perhaps that will be the subject of another post.

Hurricane Melissa (2025)

Storm Active: October 21-31

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 190 mph and a minimum central pressure of 892 mb. Melissa weakened just slightly before landfall; its estimated strength when the center crossed the shore was 185 mph winds with a central pressure of 897 mb.

Melissa's strength set a number of records. The 897 mb mark was the second lowest ever recorded for a landfalling Atlantic hurricane, behind only the Labor Day Hurricane of 1935, which recorded a landfall at 892 mb. Melissa's overall peak of 892 mb tied the same hurricane for third lowest ever recorded in an Atlantic hurricane, behind only Gilbert of 1988 and Wilma of 2005. Melissa's peak 1-minute sustained winds of 190 mph tied Hurricane Allen of 1980 for the strongest ever recorded in the Atlantic. While reconaissance aircraft were flying through the hurricane near its peak, a dropsonde instrument measured a wind gust of 252 mph a few thousand feet above sea level, which set a global record for strongest wind gust measured in a tropical cyclone.

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.

Melissa transitioned to a post-tropical system during the morning of October 31. That night, the storm passed just east of Newfoundland, still packing hurricane-force winds. Ex-Melissa continued northeastward over the northern Atlantic until it merged with another low.

The image above shows Melissa at peak intensity just before its record landfall in Jamaica during the morning of October 28.

The hot waters of the southwest Caribbean sea allowed Melissa to become one of the most powerful hurricanes in recorded history. The storm's most devastating impacts were in western Jamaica, but it also caused damage in Haiti, eastern Cuba, the Bahamas, and Bermuda.

Note that several statistics related to Melissa's peak intensity were amended during post-season analysis. The estimated peak sustained winds were upgraded from an operational estimate of 185 mph to 190 mph, tying Allen for the strongest ever in the Atlantic. The same analysis found that Melissa weakened slightly before landfall to an intensity of 185 mph winds and a pressure of 897 mb.