Thursday, June 30, 2022

The Weirdest Chess Move

This post will attempt to answer the question: "What is the weirdest possible chess move?"

More specifically, we'll consider all possible chess move notations, using standard algebraic chess notation. So among possible written moves such as "Ne6", "Qxd7", etc., we want to decide which is the most unusual. I could imagine two different ways of making "weirdest" more precise.

  1. Consider the list of all possible chess games (using standard rules), written down using standard chess notation. Which move notation occurs the fewest number of times in all possible games?
  2. Look at all tournament chess games (with standard rules, etc.) that have occurred in history. Alternatively, let a powerful chess engine such as Stockfish play itself many times and write down all the games. Which move notation occurs with the lowest frequency?
Approach (1) is at least a well-defined question, because the number of chess games is finite, though incredibly large. The reason for this is that by the 50-move rule, any chess game in which there is no capture or pawn advance in 50 moves in automatically a draw; thus pieces cannot shuffle around the board forever and every game must end. One estimate for the number of possible chess games is known as the Shannon number, named after the mathematician Claude Shannon. The estimate is 10120, which vastly exceeds even the number of atoms in the observable Universe! Therefore, it's impossible in practice to enumerate all chess games.

Approach (2) is a little better, but if we use only games that have actually occurred, or a computer sample size small enough to be computationally feasible, it might be too small for any of the "weirdest" moves to appear (we'll see this later). Moreover, we've made some choices about what a sample of representative "good" chess games might look like. I prefer approach (2), though, since the spirit of the challenge is to find what moves come up the least often in a game where both players play sensibly. In any case, my proposed "weirdest move" has not happened in any game that I could find.

The question I'm considering is a little unusual. Instead of looking at possible chess positions, the problem only asks about how a particular move is written down, so the only information we get about the position is from what the notation conveys. This includes the piece moving, the destination square, whether the move is a capture, whether it delivers a check or checkmate, etc.



For example, in the above position, black has just made the move "Nxf3+". The "N" indicates the knight has moved, "f3" is the destination square, "x" means the move was a capture, and the "+" means that the move delivers a check (but not checkmate). However, if we only see the symbols "Nxf3+" in isolation, we don't know what other pieces are on the board, where the knight came from, or where exactly the enemy king is (just that it's in range of the knight's attack).

There are some other notations for special moves in chess, such as castling: kingside castling is denoted "O-O", and queenside castling "O-O-O". The promotion of a pawn is denoted by an "=" sign, for example "e8=Q". In constrast, en passant does not have a special symbol in standard notation.



The above image shows a position after black plays "a5". This is an opportunity for white to capture en passant, meaning that white's b-pawn can move to a6 and capture the black pawn on a5 on the next move as if it had moved one square instead of two. However, this is notated simply "bxa6", so if we only know the notation and not the position, we can't distinguish en passant from an ordinary pawn capture.

Let's try a few weird moves. We'll start with castling. Castling on its own happens in almost every game, but it is usually a move to improve king safety in the opening, so it is almost unheard of to check or checkmate with a castling move. Hence, we have our first candidate weirdest move:

Candidate 1: O-O-O#

The notation here means: queenside castle and checkmate. It's an incredibly rare move, but it (nearly) happened in a high-profile historical game! In a 1912 game between international master Edward Lasker (distantly related to world chess champion Emanuel Lasker) and twice British chess champion George Alan Thomas, the following position was reached after black's 17th move, "Kg1".



Lasker had the opportunity to play checkmate in one move with "O-O-O#", our candidate weirdest move! He instead played "Kd2#", which is still checkmate since it allows the white rook on a1 to see the enemy king. Moving the king to deliver checkmate is already a bit uncommon, but the queenside castle would have been stranger still. You might be wondering how on earth the black king arrived on g1 in this game! It was in fact the culmination a remarkable series of forced moves in which the black king went from g8 to g1. The full game is well worth checking out (see here for an explanation of the full game).

Therefore, queenside castle checkmate is rare, but it did almost occur in a game involving two very high caliber players, so maybe we can do better. There's another uncommon move type that's natural to try: underpromotion.

When a pawn reaches the end of the board, it can become a queen, but the player also has the option to trade their pawn for a different piece instead (rook, knight, or bishop). This is called an underpromotion. Since the queen is the most powerful piece in chess, there are very few cases in which a player would "legitimately" underpromote, i.e. where the underpromotion is a superior move to promotion to a queen. Most occurrences of underpromotion in real games are "just for fun", for example when the promoted piece would be captured either way. However, there are some exceptions.



The above position occurred in a game between Vladlen Zurakhov and Alexander Koblents in a 1956 USSR semifinal event. Koblents has just played his knight to f5 and is threatening to win the pawn on g7, which would bring the game to a knight vs. two pawns position that is a theoretical draw. Therefore, white must promote the g pawn. However, if white plays "g8=Q", black will simply win the queen by forking the queen and king with the move "Ne7+". The only move that wins for white is "g8=N", an underpromotion to a knight. This defends against the fork, and the new knight can go on to help one of the two remaining pawns to queen promotion (this is still a difficult win, but Zurakhov did end up winning the game). Since knights can move and attack in ways that queens cannot, it makes sense that knight underpromotions are sometimes practical. Indeed, promoting to a knight is next most common after promoting to a queen. This leads us to our second candidate:

Candidate 2: Bishop underpromotion (e.g., "a8=B")

The rarest underpromotion of all is to a bishop. The bishop's value in chess is roughly equal to the knight's as the lowest of the (non-pawn) pieces, and unlike a knight, the bishop does not move in a way that the queen cannot. In particular, I didn't include a "#" (checkmate symbol) on the example move in Candidate 2, because if a bishop promotion move comes with checkmate, the same move with a queen promotion instead would also be mate. Therefore, no "legitimate" underpromotion occurs that way. I could also have made the move a check or capture, but this makes relatively little difference.

Though some endgame compositions have featured this type of move, there are once again precious few examples in real games. One of the only ones on record is in the following game between Aron Reshko and Oleg Kaminski in the 1972 Leningrad chess championship.



In this position, it's white to move. Though Reshko has a pawn close to promotion, Kaminski has a trick up his sleeve. First, if white does not address the threat on the a7 pawn, the black queen will simply win it in the next move, leading to equal material and a likely draw. If white moves to protect the pawn on its current square by taking the queen to a4 or b8, black can play the queen to f7 for checkmate!

Therefore, white must promote the pawn (or throw in a check with "Qg6+", but the queen must simply return and this gains nothing). However, promotion to a queen or a rook lead to an immediate draw because of black's defensive resource "Qf7+", sacrificing the queen! White's only move is to take the queen, and the resulting position is stalemate, a draw.



The above image shows the hypothetical variation 61. a8=Q Qf7+ 62. Qxf7. Though white is now up two full queens, black has no legal moves and the game is a draw by stalemate. A rook on a8 would also guard the h8 square, so it's again stalemate. Promoting to a knight in the initial position avoids this problem, but it's not too hard to see that the knight can't escape the corner without black's queen capturing it. The only winning strategy, which Reshko found in this position, is to promote to a bishop. Soon after, the players traded queens, and with an extra bishop, white went on to win.

While the bishop underpromotion is the rarest type of move in chess, it is not the weirdest move in terms of notation. I'll reveal my pick for the game's weirdest move in the next post.

Sunday, June 5, 2022

Tropical Storm Alex (2022)

Storm Active: June 5-6

During the last week of May, a tropical cyclone developed southwest of Mexico and became Hurricane Agatha, the first named storm of the Eastern Pacific hurricane season. On May 30, it made landfall as a category 2 hurricane in the Mexican state of Oaxaca. It caused widespread flooding in southern Mexico but the low-level center quickly dissipated over the mountainous terrain. Nevertheless, the remnants moved generally northeastward toward the Gulf of Mexico.

There was significant wind shear over the region, which prevented reformation at first. There were also two areas of vorticity: one was the remnants of Agatha, and another upper-level low farther east. It took time for these areas to consolidate. Despite this, the disturbance was quite vigorous. By June 3, when it was centered just north of the Yucatan Peninsula, the low was already producing gale force winds. The next day, it made landfall in southwestern Florida, bringing tropical storm force winds and heavy rain to the southern half of the state.

It wasn't until after the system moved east-northeastward over the open Atlantic that it finally became organized enough to be designated Tropical Storm Alex early on June 5. Alex was named quite soon after the official start of hurricane season on June 1, but 2022 was actually the first time since 2015 that there was no named storm prior to June 1.

The storm strengthened over the Gulf stream during the day and became a strong tropical storm by the evening. Alex reached a peak intensity of 70 mph winds and a minimum central pressure of 984 mb that night. Soon after, it encountered colder waters and higher shear, which weakened the cyclone and hastened its extratropical transition. Before it finished this transition, however, Alex passed just north of Bermuda early on June 6, bringing tropical storm conditions to the island. Alex was designated post-tropical later that day. The remnants merged with another low over the Atlantic just one day later.



The above image shows Alex intensifying over the western Atlantic. The U.S. east coast is visible at left.


The low that became Alex brought gale conditions to southern Flroida on June 4, but it was not yet a tropical cyclone at the time.

Tuesday, May 17, 2022

Professor Quibb's Picks – 2022

My personal prediction for the 2022 North Atlantic Hurricane season (written May 17, 2022) is as follows:

20 cyclones attaining tropical depression status,
19 cyclones attaining tropical storm status,
9 cyclones attaining hurricane status,
5 cyclones attaining major hurricane status.

This prediction is well above the 1991-2020 averages of 14.4 tropical storms, 7.2 hurricanes, and 3.2 major hurricanes each season in the Atlantic basin. I expect that 2022 will thus be the third consecutive season with significantly above-average activity. Below, I'll discuss the various factors involved in making this prediction.

The first factor to consider is, as always, the El Niño Southern Oscillation (ENSO) index, which is a numerical measure of sea surface temperature anomalies in the equitorial Pacific ocean. When these waters are warmer than normal (El Niño), Pacific tropical cyclone activity is elevated and Atlantic activity is suppressed. When they are cooler (La Niña), the reverse is true. Remarkably, La Niña conditions are expected to persist through the summer, making 2022 the third consecutive La Niña year! The graphic below shows various model predictions for the ENSO index through the rest of the year. The official threshold for a La Niña event is -0.5, and the index is expected to linger near or below this threshold by a majority of models.
Once again, it seems likely that La Niña will give this year's activity a significant boost.

The map below shows current sea surface temperature anomalies in the Atlantic. They are mostly above average, though no region in particular stands out too much. Note that sea surface temperature anomalies are generally measured relative to a mean based on the last few decades. Therefore, this does not account for anthropogenic ocean warming; measured against pre-industrial levels, these anomalies would be greater.



Until May, the main developement region (between the western African coast and the Caribbean) actually had somewhat below average sea surface temperatures. Recently, however, the east-to-west trade winds have relaxed. When trade winds are strong, they churn up cooler ocean waters from below the surface; they also directly inhibit cyclone formation by making it hard for vortices to form (see here for more). Therefore, recent trends are concerning, as the eastern Atlantic has warmed significantly in the last month. If this continues, long-track hurricanes are likely by the heart of the season. Finally, we'll take a look at the following prediction for wind shear anomalies in the first half of hurricane season (June-July-August).



Blue indicates below-average wind shear and hence more favorable conditions for hurricanes to form. The signal in this model is quite strong; it seems likely that the Caribbean in particular will have little wind shear during early hurricane season. Note that below-average shear is consistent with a La Niña pattern, but this doesn't occur everywhere: in the deep tropics near Africa, there's an area of above-average shear. In this model, the region of above-average shear even drifts northward as the summer progresses. Nevertheless, almost all factors point to a quite active hurricane season.

Using these and a few other factors, 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: 4
Most areas are at above-average risk this year, and the east coast is no exception. The good news is that I expect most of the cyclones forming in the main development region during August and September will curve out to sea, since the shear pattern favors the consolidation of tropical waves more at their northern ends. Storms forming closer to home will be the ones to watch for.

Yucatan Peninsula and Central America: 4
The monsoon in this region is currently quite active. This elevates the risk for some messy tropical storms near central America in late May and June, with flooding and mudslides the main concern. It's difficult to say this early, but October and November may also be an active time for the western Caribbean.

Caribbean Islands: 4
All the general factors discussed above also suggest the Caribbean will be at elevated risk, but I don't see anything specific pointing to tracks through the islands. I do expect an early start to activity in the region, with multiple storms by the time August comes around.

Gulf of Mexico: 5
The Gulf coast has experienced an exceptional number of hurricane landfalls already during the 2020 and 2021 seasons. With the La Niña continuing, this is unlikely to abate this year, unfortunately. The atmospheric setup on models this year also seems to favor steering cyclones into the Gulf, should they form in the Caribbean. This merits a maximum risk designation.

Overall, I expect the 2022 Atlantic hurricane season to be well above 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://www.cpc.ncep.noaa.gov/products/analysis_monitoring/lanina/enso_evolution-status-fcsts-web.pdf, https://www.tropicaltidbits.com, https://www.trackthetropics.com/saharan-air-layer-sal-tracking/, https://www.nhc.noaa.gov/sst/

Saturday, May 14, 2022

Hurricane Names List – 2022

The name list for tropical cyclones forming in the North Atlantic basin for the year 2022 is as follows:

Alex
Bonnie
Colin
Danielle
Earl
Fiona
Gaston
Hermine
Ian
Julia
Karl
Lisa
Martin
Nicole
Owen
Paula
Richard
Shary
Tobias
Virginie
Walter

This list is the same as that for the 2016 season, with the exception of Martin and Owen, which replaced the retired names Matthew and Otto, respectively.

Saturday, January 1, 2022

Zodiacal Light

Looking east on a clear night, just before sunrise, a glow extends upward from the horizon. This light lingers, coexisting with the stars, before a brighter band of sky appears along the horizon, the Sun itself not far behind. Long exposure photography shows the phenomenon clearly, such as in the left side of the image below (the glow of the Milky Way galaxy is also visible on the right).



Astronomers first noticed the subtle first light, known as zodiacal light, centuries ago. In fact, identifying this phenomenon has been important to the practice of Islam. The fajr, or dawn prayer, is required before sunrise every day, but how long before? Unlike noon and sunset, the time of dawn is harder to pin down precisely.

The phenomenon of zodiacal light was significant enough to be named in the teachings of the Islamic prophet Muhammad: it was called "the false dawn", al-fajr al-kazib, to be distinguished from the later "true dawn", al-fajr as-sadiq. The latter time is widely accepted to be the correct one for the dawn prayer.

But what causes this light? In some ways, the cause is mundane: astronomers have long known that the glow originates from sunlight reflecting off of small dust particles in space. The long-narrow shape of the glow occurs because dust is not distributed uniformly throughout interplanetary space. Nearly all objects orbiting the Sun, from the largest planets to the smallest dust particles, cluster near a single plane, the plane of the Solar System. In our night sky, this plane appears as a line known as the ecliptic, along which the planets, Sun, and Moon travel. In turn, the constellations on the ecliptic are known as the zodiac. Voilà! Zodiacal light! Though most pronounced near the Sun at dawn, dim zodiacal light can be observed on a moonless night to follow the entire ecliptic.

However, this explanation merely raises another question. Where does the dust come from? Some debris comes from comets and asteroids, but some more evidence recently surfaced on this subject from an unlikely source.


On August 5, 2011, the NASA spacecraft Juno launched from Earth, the beginning of its five-year journey to Jupiter. Elsewhere on this blog, I've written in depth about Juno's mission and its many discoveries orbiting the Solar System's largest planet. However, the probe began gathering important data long before reaching its destination. Along its trajectory (pictured above*), Juno returned to Earth for a gravity assist to give it a boost to Jupiter. During its journey, scientists on the Juno team noticed something alarming: thousands of tiny streaks of light appeared on images of what should have been empty space!

Further analysis revealed that the streaks were tiny bits of debris knocked from Juno's solar panels, dislodged by microscopic dust particles impacting at high velocities. Unintentionally, the large solar panels of Juno became a interplanetary dust collector! Fortunately, the impacts were not large enough to cause damage detrimental to the mission, but they did reveal a surprising story.



In all, over 15,000 dust impact events were recorded, enough to measure in unprecendented detail the distribution throughout the inner Solar System. The figure above* (click to enlarge) shows the data. The top panel shows events on Juno's inbound stage from the farthest point of its first orbit (on the trajectory image, the point marked DSM or "Deep Space Manuever") to Earth flyby. The second shows impacts recorded outbound from Earth flyby through the asteroid belt, on its way to Jupiter. The horizontal axis measures distance from the Sun, while the black line indicates frequency of imapct events. For context, various significant distances and the distribution of asteroids (gray) in the asteroid belt are also included.

As a bonus, the outbound portion of the trajectory shown above was tilted from the ecliptic plane, while the inbound one lay within it (see again the trajectory image). Hence, we can clearly see that less impacts occur away from the plane of the Solar System. It is also clear that the impacts are reduced near Earth, since our planet's gravitational influence "clears its orbit" of dust. Nevertheless, it is the dust closest to us that causes most of the zodiacal light we observe.

In contrast, the vicinity of Mars appears riddled with dust, even more so than some parts of the asteroid belt! This was a great surprise, for it was expected most of the dust was from asteroids and that Mars would clear its orbit, just like Earth does. However, further data analysis confirmed that Mars must in fact be a major source of the dust that ultimately causes zodiacal light! There is much more to be discovered about this story: what mechanisms cause Mars to lose so much dust to space? Currently, the answer is not definitively known, though further space missions could provide clues. But after thousands of years of mystery, at least we now know that when we see that before-dawn glow, we have the red planet to thank.

Sources: https://www.al-islam.org/articles/al-fajr-sadiq-new-perspective-sayyid-muhammad-rizvi, https://earthsky.org/astronomy-essentials/everything-you-need-to-know-zodiacal-light-or-false-dusk/, https://agupubs.onlinelibrary.wiley.com/doi/epdf/10.1029/2020JE006509, https://www.jpl.nasa.gov/news/serendipitous-juno-detections-shatter-ideas-about-origin-of-zodiacal-light

*The last few figures in this post are from the paper "Distribution of Interplanetary Dust Detected by the Juno Spacecraft and Its Contribution to the Zodiacal Light" by J. Jorgensen et al.

Monday, December 13, 2021

2021 Season Summary

The 2021 Atlantic hurricane season was quite active, with a total of

21 cyclones attaining tropical depression status,
21 cyclones attaining tropical storm status,
7 cyclones attaining hurricane status, and
4 cyclones attaining major hurricane status.

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

17 cyclones attaining tropical depression status,
16 cyclones attaining tropical storm status,
8 cyclones attaining hurricane status,
5 cyclones attaining major hurricane status.

The average numbers of tropical storms, hurricanes and major hurricanes (over the 30 year period 1991-2020) were 14.4, 7.2, and 3.2, respectively. This puts the 2021 season a bit above average overall, with a much higher than usual number of named storms but near average numbers of hurricanes and major hurricanes. Likewise, my predictions underestimated the number of named storms, but were close on hurricanes and major hurricanes. The 21 named storms were the third-most recorded for an Atlantic season at the time, behind 2020 and 2005. The Accumulated Cyclone Energy (ACE) value for the 2021 season (which accounts for duration and intensity of storms as well as number) was roughly 145, once again above normal but not by a huge margin. The exact figure will likely shift slightly in post-season analysis.

A bevy of short-lived, weak systems inflated the total number for the season, especially early on. There were three named storms in June for the first time since 1968. Hurricane Elsa set a record for earliest fifth named storm when it was named on July 1. However, the end of the season was surprisingly quiet. With the exception of meandering Tropical Storm Wanda, which spent a week in early November moving around the north Atlantic, there was no activity from October 4 onward. This is quite unusual: on average, one would expect around 3 named storms and at least 1 hurricane during that time. Even stranger, the entire world experienced a lack of strong cyclones during October and November 2021. To explain this behavior, we'll examine a few factors.


At the beginning of the season, an ongoing La Niña event was on the wane, and indeed it officially ended over the summer. However, equatorial Pacific sea temperature anomalies remained negative (consistent with La Niña) and even began to decrease again by late in the year. The relevant regions of the Pacific and their temperature anomalies throughout the year are illustrated above. Overall, the weak La Niña that occurred was consistent with pre-season predictions. It is correlated with lower wind shear in the Atlantic and thus consistent with the somewhat above normal activity observed. Likewise, the tropical north Atlantic had fairly warm ocean temperatures, which helped tropical cyclones to form and intensify. However, this doesn't explain why the Atlantic shut down in October.



2021 featured a particularly strong west African monsoon; note the high precipitation over Africa around 10° N or so between June and August in the map above. This is signficant because tropical waves, the precursors to most Atlantic tropical cyclones, form over Africa and move westward into the Atlantic. Indeed, in contrast to 2020, a larger proportion of storms originated in the tropical Atlantic (see the map of storm tracks below):

Every year, the opportunity for cyclone formation off of Africa closes in early October, when the wave axis shifts toward the equator and east Atlantic temperatures start to get cooler. The center of activity usually then shifts to the Caribbean, but the Caribbean saw an unusual amount of dry sinking air late in the year, stifling any formation. This is again in stark contrast to 2020, when the west Caribbean saw its most active period in recorded history from October through November. These factors help to indicate why the 2021 season ended earlier than expected.

In my predictions, I put the Caribbean islands and the Gulf of Mexico at highest risk, with the U.S. east coast and central America at lower risk. These predictions were fairly good: Hurricane Elsa, Tropical Storm Fred, Hurricane Grace, and Hurricane Ida impacted the Caribbean Islands, while Ida and Hurricane Nicholas had the greatest Gulf impacts (though Grace also hit the Yucatan and the southwest Gulf). The Caribbean impacts might have been greater still had some of the above storms not tracked directly over the greater Antilles. No landfalls occurred in central America and only the extremely unusual Henri had any significant impact on the U.S. east coast as a tropical cyclone.

Some other notable facts or records from 2021 include:
  • Tropical Storm Ana's formation on May 22 made 2021 the seventh consecutive season with a named storm before June 1
  • Elsa was the easternmost forming early July hurricane in the tropics since 1933; it also had the highest forward speed of any known Atlantic hurricane in the tropics
  • Grace's remnants reformed as a tropical storm in the eastern Pacific and were named Marty
  • Henri was the slowest-moving cyclone ever recorded in the U.S. northeast; this led to unusual flooding impacts in the region
  • Ida tied 2020's Hurricane Laura for highest winds of a landfalling Louisiana hurricane (150 mph)
Finally, Hurricane Sam was the season's strongest storm, with winds of 155 mph and a central pressure of 929 mb. It was a long-lived and powerful storm, clocking in at over 50 ACE just on its own and holding major hurricane status for 7.75 consecutive days. Despite this, it went out to sea and didn't significantly impact any landmasses.

The 2021 season was quite active, though with many weak systems. The vast majority of the season's damage and loss of life were due to Hurricane Ida, which made landfall in Louisiana as a category 4 hurricane.

Sources: https://www.washingtonpost.com/weather/2021/11/22/earth-hurricane-activity-record-quiet/, https://www.cpc.ncep.noaa.gov/products/analysis_monitoring/lanina/enso_evolution-status-fcsts-web.pdf

Tuesday, November 2, 2021

Tropical Storm Wanda (2021)

Storm Active: October 30-November 7

On October 25, an early-season nor'easter formed off the United States east coast. The low deepened rapidly over the next day and brought hurricane-force wind gusts to coastal Massachusetts, but it was a non-tropical system. The system meandered near the coast for another day before slowly retreating eastward over the open Atlantic. It remained an intense low for the next several days, but was still attached to a frontal boundary. The low moved turned southeastward on the 27th and pursued that heading for a few days until it encountered warmer waters. Late on the 30th, the cyclone was classified as Subtropical Storm Wanda; it had more central convection and a tighter windfield, but was still interacting with nearby fronts.

After formation, Wanda slowed down and meandered across the open central Atlantic. Meanwhile, the cyclone was separating further from the nearby upper-level low. It transitioned into a fully tropical storm on November 1.

Wanda turned northward and made some steady progress in that direction over the next few days, following a trough to its north. The convective structure remained somewhat subtropical in appearance, with curved bands north and west of the center, but little in the way of deep central convection. However, on November 4, a ridge built to the north of Wanda and turned it back southeastward, in the general direction of the Azores.

By November 6, Wanda began to feel the pull of a powerful cyclone over the north Atlantic. It turned back to the northeast and began to accelerate, passing northwest of the Azores. The cyclone encountered high shear and colder waters and transitioned to an extratropical cyclone on the 7th.



The above image shows Wanda on November 3 over the open Atlantic.


Wanda took a meandering track over the north Atlantic, beginning as an extratropical low near the Eastern seaboard and ending past the Azores.

Wednesday, September 29, 2021

Tropical Storm Victor (2021)

Storm Active: September 29-October 4

On September 27, a tropical wave moved off of Africa into the eastern Atlantic. It was located on the eastern edge of a monsoonal trough of low pressure, while another tropical wave was situated on the western end. For a few days, these disturbances battled it out, but the eastern one ultimately became dominant and organized into Tropical Depression Twenty on September 29. It was located in quite favorable conditions, but its large size kept strengthening gradual. The depression became Tropical Storm Victor later that day. It was the second earliest formation of a twentieth named storm on record, behind only Vicky of the previous year, which formed on September 14. Victor was named at an unusually low latitude for the Atlantic at 8.3° N.

Despite forming close to the equator, the storm gained latitude steadily as its trajectory bent from west-northwest to northwest due to the influence of an upper-level low in the subtropics eating away at the ridge that usually steers such storms west. Meanwhile, Victor managed to consolidate a little and strengthen into a high-end tropical storm with maximum winds of 65 mph and a central pressure of 997 mb. However, on October 1 it moved into the sphere of influence of the aforementioned upper-level low, which began to impart strong wind shear. At the same time, Victor reached a drier airmass. The storm steadily weakened from there on out.

The storm became a tropical depression on October 2, but intermittent convective bursts allowed it to remain a tropical cyclone for a while after that. Wind shear degraded the circulation gradually and Victor at last degenerated into a trough of low pressure on October 4.



The above image shows Victor at peak intensity, when it was already dealing with increasing shear and dry air intrusion.


During most of September, the steering pattern over the tropical Atlantic allowed tropical cyclones to escape northward, out to sea. Victor followed this pattern, avoiding land areas.

Saturday, September 25, 2021

Subtropical Storm Teresa (2021)

Storm Active: September 24-25

On September 23, a surface trough formed in conjunction with an upper-level low that was producing a huge area of scattered thunderstorm activity in an arc east and south of Bermuda. The system consolidated some over the following day as it moved generally northward and a well-defined surface center appeared north of Bermuda. The island experienced only minor impacts as the disturbance passed near it. There was some deep convection too, though it was generally located north and east of the center of circulaton. The storm was non-frontal. However, it was still located under an upper-level low and furthermore did not look much like a conventional tropical storm: thus, it was classified Subtropical Storm Teresa. Teresa was the second earliest nineteenth named storm (typically, "T" storm) on record, after only Teddy of 2020.

The storm's genesis was not well-anticipated, and it only had a small window for intensification, as a powerful extratropical low was forming near New England. Teresa was heading northwest initially, and then turned north and then northeast as it became caught up in the low. Increasing shear overwhelmed the storm and it became post-tropical on September 25. The low lost its identity soon after.



Teresa's satellite presentation looks distinctly subtropical, with little convection near the center and an asymmetric appearance.


Teresa added to the list of short-lived cyclones of the 2021 season.

Wednesday, September 22, 2021

Hurricane Sam (2021)

Storm Active: September 22-October 5

A tropical wave exited Africa into the Atlantic on September 19. Finding favorable conditions, it began to organize, and a spin was soon evident on satellite imagery. It stayed pretty far south, missed Cabo Verde, and moved west over the next few days. By the 21st, a low had formed, but the disturbance didn't have the closed circulation center necessary to be called a tropical cyclone. One more day was enough for the system to become Tropical Depression Eighteen.

It took another day or so for the new tropical cyclone to start intensifying, but after that it was off to the races. On September 23, it strengthened into Tropical Storm Sam, which was the second earliest an eighteenth named storm had ever formed on record in the Atlantic (Sally of 2020 was the record-holder). Sam had a small core, which allowed it to quickly vault to hurricane strength on the 24th. There was little wind shear in the system's vicinity, and waters were plenty warm to support development; the moderately dry mid-level air around the storm was unable to penetrate it and slow down the intensification process. By the afternoon of September 25, Sam reached category 4 intensity.

After having moved west for a few days, Sam had slowed down and turned west-northwest under the influence of a weak subtropical ridge. Indeed, the ridge was so weak that Sam's forward motion was unusually slow for a hurricane in its location. The storm was still small enough that cold water upwelling didn't present a significant issue even with the lower forward speed. The cyclone had a small, symmetric eye surrounded by extremely cold cloud tops and managed to reach a peak intensity of 155 mph winds and a central pressure of 929 mb during the afternoon of September 26. Right afterward, the eye contracted and dry air forced its way into the center from the east during an eyewall replacement, causing sudden rapid weakening. This brought Sam down to category 3 by the 27th.

As the storm continued northwest, it fought back, restrengthening to category 4 the next day. Its structure was quite different, with a larger, less symmetric eye, and a larger radius of maximum winds. On September 29, it made its closest approach to the Lesser Antilles, passing well to the northeast. The next day, Sam begin to speed up and turn north as it rounded the subtropical ridge. Remarkably, the storm continued intensifying, reaching its secondary peak intensity of 150 mph winds and a central pressure of 934 mb early on October 1.

Overnight, Sam made its closest approach to Bermuda to the south-southeast; the island was far enough away to be spared significant impacts. Gradual weakening commenced as the storm recurved, but its tropical storm force windfield continued to expand. Early on October 3, Sam finally lost major hurricane strength after being category 3 or above for 7.75 consecutive days, joining only a small handful of Atlantic hurricanes to achieve this feat. Later that day, as it moved northeast toward the north wall of the Gulf stream, the eye cleared out again and became symmetric, with well-defined concentric eyewalls. This resulted in some restrengthening that evening near 40° N! The storm's structure was exceptional for that latitude. At last, on October 4, Sam encountered much colder water and began extratropical transition. As the inner core decayed, Sam weakened to a category 1. The storm became a hurricane-force extratropical low early on October 5 and merged with another low over the far north Atlantic soon after.



The above image shows Sam at its peak intensity on September 26.


Sam's long track as a major hurricane made it one of the largest Accumulated Cyclone Energy (ACE) producers recorded. Despite its longevity, Sam didn't affect any landmasses except Bermuda, to which it only delivered a glancing blow.