Sunday, March 26, 2017

More Evidence for Planet Nine

For the first post in this series, which explains the motivation for the Planet Nine hypothesis, click here.

The previous post touched on some ways in which the orbits of certain outer Solar System objects are similar. These may be quickly summarized in the following way: both the arguments and longitudes of the objects' perihelia are unusually clustered around certain values.

The above image shows numerous relevant parameters concerning the position of an orbit. In the case of orbits in the Solar System, the plane of reference is the plane of the Earth's orbit and the Sun, also known as the ecliptic. The reference direction often used for heliocentric objects is called the First Point of Aries, defined as the position of Earth's vernal equinox and so named for its location within the constellation Aries. The ones with which we are concerned here are the argument of periapsis ω (this is the general name for argument of perihelion to include non-heliocentric objects) and the longitude of the ascending node Ω. The sum of these two angles is called the longitude of perihelion because it measures the angle between the perihelion and the reference direction. In summary, the similarity in the arguments of perihelion indicates that the members of the relevant population of objects have similar orientations with respect to the plane of the Solar System, while the similarity in the longitudes indicates a clustering of these orbits in space.

A 2016 paper by Konstantin Batygin and Michael E. Brown ran a statistical analysis of these parameters for the six most extreme known trans-Neptunian (beyond Neptune) objects. Since they were discovered by a number of distinct observational surveys, the possibility of observational bias was dismissed. The analysis found that the clustering of the objects had only a 0.007% probability of occurring by chance. This suggested that another explanation was in fact required for the phenomenon. Further simulations suggested that a Planet Nine could account for the observations, provided that it have the required heft: at least around 10 Earth masses (or, equivalently, 5000 Pluto masses). In comparison, all the previously known trans-Neptunian objects put together weighed much less than a single Earth mass.

Shortly afterward, more evidence for Planet Nine was discovered, using data from a surprising source: the Cassini space probe. Launched in 1997, this Saturn orbiter allowed the calculation of the position of Saturn over time to unprecedented precision. These were compared to an extremely precise gravitational model of the Solar System known as INPOP, which accounts for the gravitational influence of the Sun, the planets, and many asteroids. The model then outputs planetary ephemerides, namely positions of the planets at given times. A paper published in February 2016 by Agn├Ęs Fienga et al. experimented with adding a Planet Nine at different positions to the INPOP. If the residuals (differences in Saturn's position between the predictions of INPOP and the real measurements from Cassini) are increased, this rules out the existence of Planet Nine in this position. However, if they are decreased, then this is evidence in support of Planet Nine, since it would partially explain the observed discrepancy.

The results of the paper are summarized in the diagram above. They showed that Planet Nine of 10 Earth masses and a semi-major axis of 700 AU was ruled out by Cassini's data to be in the red zones (this increased the residuals). The pink zones correspond to areas that would be ruled out by further inclusion of Cassini's data (the paper only used the measurements through 2014). The green zone, however, is where a Planet Nine would decrease residuals, making the INPOP model a more accurate picture of the Solar System. Therefore, the paper found this to be the most likely zone to find Planet Nine (with the single most likely position indicated). The addition of a Planet Nine in the farther regions of its orbit would not produce significant perturbations, and thus this is labeled "uncertainty zone".

Further analysis fine-tuned the estimates of mass, eccentricity, semi-major axis, and other parameters for the supposed Planet Nine. With an array of increasingly large telescopes at their disposal, astronomers will soon be able to settle the Planet Nine hypothesis one way or the other, bringing new insight into the current structure and the formation of our Solar System.


Sunday, March 5, 2017

The Planet Nine Hypothesis

Beginning in the 1990s, advances in astronomy allowed the detection of many extrasolar planets, adding thousands of the number known within two decades. However, apart from the reclassification of Pluto as a dwarf planet in 2006, the population of true planets in our Solar System did not change. Many, many other smaller objects were discovered, though.

Many of these smaller objects lay within the asteroid belt between Mars and Jupiter, or in the Kuiper Belt, just beyond Neptune's orbit. Eris, Haumea, and Makemake are other dwarf planets whose perihelia (closest approaches to the Sun) bring them within the Kuiper Belt, 30 to 50 astronomical units (AU) from the Sun. However, an unusual object was discovered in 2003 whose orbital properties were quite different.

The object was later named Sedna and measures a little less than half the diameter of Pluto. Though the best images of it by telescopes are only a few pixels wide, it is clearly of a reddish color, nearly as red as Mars. The perihelion of this object was, at the time, the largest known in the Solar System, at 76 AU. However, it also has an extremely elongated orbit, bringing it to an aphelion (farthest point) of 936 AU! This orbit is shown in red above, compared to the orbits of the outer planets and Pluto (in pink). About a decade later, another object, provisionally designated 2012 VP113, was discovered with comparable orbital parameters, except with a slightly farther perihelion of 80 AU and an aphelion of 438 AU. The scarcity of known objects of this type is not only a consequence of their distance, however.

This scatterplot, published in a paper by astronomers Chadwick A. Trujillo and Scott S. Shephard, shows the perihelia and eccentricities (a measure of the "elongatedness" of an elliptical orbit; a perfect circle has an eccentricity of 0) of various objects outside Neptune's orbit. Curiously, there is a clear drop-off at around 50 AU, with only a few known objects beyond. Notably, there is also a gap between 55 and 75 AU. This gap is not only an artifact of our telescopes being insufficiently powerful: Sedna and 2012 VP113 were detected farther out, so if there were objects in this gap they should have been easier to find. The high eccentricity of Sedna and 2012 VP113, as well as the existence of this gap, aroused suspicion that a massive object may have gravitationally perturbed the trajectories of objects in this region, illustrated in the image below.

The same paper indicated another unusual feature of the population of these farthest known objects.

The horizontal direction indicates the semi-major axis of each object (yet another measure of the size of an orbit; however, it is closely related to the two discussed previously: it is simply the average of the perihelion and the aphelion). The vertical variable on the scatterplot is the argument of perihelion, which is simply the angular position around the orbit of the orbit's perihelion (relative to where it crosses the plane of the Solar System). All known objects whose semi-major axes exceed 150 AU have arguments of perihelion all clustered roughly around 0°. In the eight-planet Solar System model, this should not be the case: gravitational perturbations from the gas giants would randomize the arguments of perihelion over millions of years. However, a large planetary body orbiting well beyond the known planets could constrain the arguments of perihelion. This led to the hypothesis of a new planet, nicknamed Planet Nine.

The above image shows the orbits of many of the same objects represented by dots to the right of the black line in the scatterplot. Note how in addition to the clustering trend noted above, the perihelia are also all on the same side of the Sun. The figure also shows where Planet Nine would possibly orbit given the positioning of those objects. The story of the Planet Nine hypothesis continues in the next post.


Sunday, February 12, 2017


Rainbows are among the most recognizable of atmospheric phenomena. They appear in situations in which there are water droplets in the air during a period of sunshine. As a result, they commonly occur after rainstorms. Before exploring the properties of rainbows, we cover atmospheric optics in the absence of water droplets. This situation is dominated by Rayleigh scattering, which makes our sky blue.

Rayleigh scattering of the sun's rays occurs when sunlight strikes air molecules. Higher frequencies of light (green, blue, violet) are more readily scattered than lower ones (red, orange, yellow) so when we look at the sky away from the Sun, most of what we see is scattered blue light. The interaction of sunlight with much larger water droplets is categorically different. Instead of scattering, light traveling from air to water (or for that matter, across the boundary of any two different media) is refracted.

This means that the angle of the light ray to the normal (the perpendicular to the boundary between media) changes as it passes from one to another. The origin of this effect is the fact that light travels at different speeds through different media. The extent to which this occurs for different substances is measured by a medium's index of refraction, often denoted n. If two media have indices of refraction n1 and n2 then the angles of the light rays to the normal within each (denoted θ1 and θ2) are given by Snell's Law:

n1sinθ1 = n2sinθ2

For air and water, the indices take values nair = 1.000293 and nwater = 1.330. Snell's Law then yields the fact that light rays bend toward the normal as they pass from air to water and do the opposite upon exiting. However, these values of the indices of refraction are for a specific wavelength of light (actually a standard color of yellow light emitted from excited atoms of sodium with a wavelength of 589.3 nm). The degree of refraction varies slightly across the visible wavelengths, leading to the separation of colors that we observe as a rainbow. The small droplets of water in the atmosphere are roughly spheres, leading to the kind of refraction illustrated below:

Note that the angles by which the light rays are refracted depends on where it hits the drop (the redness of the lines has no significance in this image) since the boundary between water and air is spherical, rather than flat. Each of the rays shown undergoes a single internal reflection before emerging from the water droplet, though some light just passes through, and some is internally reflected multiple times (more on this later). However, the maximum angle between the incoming and outgoing rays are different for different colors of light: in particular, they are greater for longer wavelengths than shorter. Therefore, at the very highest angles, the colors are separated.

At one end of the spectrum, violet light has a maximum angle of 40° from the incoming light ray, while in the longest visible wavelengths, red light has a maximum angle of 42° (left). As a result, for a fixed observer, red light will appear to come from a certain angle in the sky, while violet will appear to come from another (right). Orange, yellow, green, blue, and indigo will appear in between. The result is what we see as a rainbow.

Several properties of rainbows follow directly from this understanding. The first is that all (primary) rainbows are of the same angular size in the sky, namely 42° in radius. A rainbow therefore does not have a fixed position and appears the same size to every observer, meaning that every observer in fact sees their own rainbow. Also, the center of the rainbow's circular arc must be opposite to the position of the Sun in the sky. This point is called the anti-solar point and must always be below the horizon (since the Sun is above). As a result, the higher the Sun is in the sky, the lower the (primary rainbow). If the Sun is more than 42° above the horizon, it cannot be seen at all. This is why rainbows are typically seen early in the morning or later in the afternoon. In addition, though the maximum angle is 40-42° for different colors of light, some light (of all colors) is reflected from raindrops at smaller angles, making the sky just inside the rainbow noticeably brighter. This effect is apparent in the image above.

Though most light reflected within the raindrop undergoes only a single internal reflection, some is in fact reflected more than once, leading to what are known as higher-order rainbows, notably the secondary rainbow.

The colors of the secondary rainbow are reversed since an additional reflection inside the drop reverses the color spread. Further, it is situated at 52°, outside the primary rainbow, and is considerably fainter.

The secondary rainbow is sometimes too faint to be visible, but it is always there. In fact, light can reflect internally even more, producing higher-order rainbows. However, three reflections sends the light on a path at about 43° inclined from its original trajectory, meaning that it would form a circle of this radius around the Sun. Due to its faintness and proximity to the Sun, it is very difficult to photograph, but photographs have recently captured this phenomenon (see below).

Thus, a simple application of atmospheric optics may explain the rainbow, the beauty of which has captivated humanity since antiquity.


Sunday, January 22, 2017

Solar Sails

Solar sailing is a method of propulsion in space that utilizes solar radiation to accelerate a spacecraft, reducing the amount of fuel required for interplanetary missions.

The key to solar sailing is that light, though it has no mass, does have momentum! At first, this seems contradictory; the typical (Newtonian) definition of momentum that one first learns is that momentum equals mass times velocity, or p = mv (p denotes momentum). The mass m is simply a number indicating the quantity of matter in a given object, while p and v are vector quantities, having both magnitude and direction.

However, this definition of momentum is only approximate. Einstein's theory of special relativity holds that momentum, energy, and mass are all different aspects of a single quantity. The famous mass-energy equivalence E = mc2 (c is the speed of light) captures part of this relation. However, this equation is actually a special form of a more general expression for energy:

where p is momentum and m0 is the rest mass of an object (objects which are moving have additional mass and therefore additional energy by the mass energy relation). Photons, the particles of light, travel at the speed of light and are in fact never at rest. However, since objects with a nonzero rest mass can never reach the speed of light, it makes sense to classify photons as massless. Since m0 = 0, the equation reduces to E = cp, or p = E/c. Furthermore, light has energy, so it must have momentum. Different frequencies of light have different energies so photons of greater frequencies (such as X-ray or gamma ray photons) have correspondingly greater momentum.

Considering ordinary molecules for a moment, the macroscopic phenomenon of pressure (for example air pressure) emerges from individual collisions of particles with a surface such as the surface of a balloon. The average force that air molecules colliding with a surface exert is the pressure on that surface. Moreover, each of these collisions involves a transfer of momentum: a particle bouncing from a surface reverses the direction of its momentum vector so by the conservation of momentum the deflecting object also experiences a change in momentum. A similar momentum transfer occurs when light impacts a surface, creating what it known as radiation pressure.

The reason we do not feel radiation pressure whenever we enter sunlight is simply because this pressure is minute relative to the other forces we feel, dwarfed even by the force of a single tissue resting on a surface. The atmospheric pressure at sea level, around 100 pascals (Pa), is over ten billion times greater than the radiation pressure on a perfectly reflecting surface in direct sunlight on Earth (around 10 μPa = 10-5 Pa). Note that this phenomenon is distinct from what is called the solar wind, a term which refers to the stream of particles with mass constantly emanating from the Sun. These particles also exert a pressure when they collide with objects in space, but it is over a thousand times smaller than even the minute radiation pressure. Despite the apparent insignificance of radiation pressure, as in the case of ion propulsion, even small forces add to significant acceleration in space over time.

The concept of using radiation pressure as a means of propulsion is the foundation of the solar sail. Its design is simple: a large sheet of lightweight, reflective material surrounds the spacecraft payload (as in the artist's conception above). Notably, it is desirable for the sail material to reflect rather than absorb photons because this increases the acceleration of the sail.

The concept of a solar sail dates back to shortly after Maxwell's theory of electromagnetism was established in the 1860's in the works of Jules Verne. However, its first applications in spaceflight occurred almost 150 years later. Radiation pressure was used to save fuel in minor maneuvers on the MESSENGER mission and to compensate for a loss of maneuverability in the Kepler space telescope. However, the first true solar sail was IKAROS (Interplanetary Kite-craft Accelerated by Radiation of the Sun), a spacecraft launched by the Japanese Aerospace Exploration Agency (JAXA) in 2010 to demonstrate the technology.

IKAROS's solar sail measured 20 meters across the diagonal with a reflective film only 0.0075 mm thick that incorporated 0.025 mm thick solar cells to power the telemetry and steering instruments. The orange panels around the edges of the sail steered the craft by altering their reflectance with liquid crystal reflectors. For example, if one side of the sail were made more reflective then the opposite sides, the radiation forces would differ across the sail, causing it to rotate.

Launched on May 21, 2010, the IKAROS payload weighed only 310 kg and its cylindrical body measured on 1.6 meters in diameter and 0.8 meters in height. After reaching space, it followed the above procedure to release the sail (click to enlarge). By taking advantage of the centrifugal forces on four "tip masses" at each corner of the sail, the continually rotating apparatus can expand to full diameter and remain there without any rigid structure supporting the sail. The mission was a full success, demonstrating telemetry, propulsion, navigation, and attitude control for a solar sail.

Over the following years, NASA and the Planetary Society launched their own solar sails into Earth orbit for further testing demonstration of the technology, but IKAROS remained more significant as the first interplanetary solar sail. Once in space, craft employing solar sails do not have to carry any additional fuel, greatly reducing the amount of weight necessary for interplanetary missions. These sails may soon realize their potential as an inexpensive and efficient means of exploring the Solar System.


Sunday, January 1, 2017

Voronoi Diagrams and Metrics

In mathematics and visual art, a Voronoi diagram is a type of partition on a surface (usually a plane). Such a diagram is determined from some set of points (called "seeds") on the surface and a notion of distance on the surface by assigning each point a "cell," namely the region in the plane within which the given seed is closer than any other seed. The diagrams are named for the Ukrainian mathematician Georgy Voronoy.

Our first example of a Voronoi diagram consists of only two seeds (the black dots) and two cells, where the line connecting the two seeds is also shown. The maroon region contains the points in the plane closest to the left-hand seed, and the blue region the right. The divider between the two regions bisects the line between the two seeds (since the midpoint is by definition equidistant from the two endpoints) and is in particular the perpendicular bisector of this line. We now present a more complicated example.

In this image, the dots again represent the seeds, while the differently colored regions are the cells of the diagram. The inner region is bounded by a polygon (specifically a pentagon) whose sides are perpendicular bisectors of the lines connecting each of the outer seeds to the center seed. Note also that the central region is finite, since the center seed is surrounded by other seeds, while the other regions extend outward forever. Finally, each point at which three regions meet is the circumcenter of the triangle formed by three nearby seeds. The image below illustrates this fact for our example with six seeds.

Three of the seeds have been connected to form a triangle (white). The circumcenter of the triangle is the center of the circle containing the triangle's three vertices (black). By the definition of a circle, the circumcenter (red) is equidistant from the three seeds and is therefore the point at which the three neighboring regions meet.

Further, regular patterns of seeds produce correspondingly regular patterns of the cells. For example, a repeating square lattice of points produces a repeating pattern of square cells, as shown below.

The reader may experiment with different seed placements using the interactive feature found here. There are many ways to generalize the Voronoi Diagram concept beyond the two-dimensional plane. For example, it is possible to construct three-dimensional Voronoi diagrams, again using points as seeds, except that space will now be divided into three-dimensional cells instead of two.

The above image shows a number of seeds scattered in three-dimensional space and a single cell corresponding to the seed at the center. The lines connecting the center seed to the surrounding ones are also shown. Instead of a polygon, the cell is a polyhedron, bounded by faces which are sections of the planes that form the perpendicular bisectors of the line segments connecting the seeds.

In mathematics, Voronoi diagrams are useful for visualizing the notion of a metric. Metrics are generalizations of the familiar concept of distance to a number of different spaces in addition to the normal Euclidean plane and space (which we have worked with so far). For example, consider the surface of a sphere, such as the Earth. Typically, we define the distance between two points to be the length of the straight line connecting them (which in Euclidean space is the shortest path between the points). However, given two points on the Earth (a sphere), the line connecting them might go through the interior. When we speak of "distance" on the sphere, we want the shortest path along the surface between the two given points, or in other words the fastest travel route from one to the other!

The shortest distance between the points A and B above on the sphere is not the latitude line that they share (though this would be the straight path between them on the 2D map projection) but the arc of a circle passing through the sphere's center. These circles are known as great circles. The distance between two points on a sphere is defined to be the length of the great circle arc connecting them. This is also why planes take what appear to be inefficient paths on two-dimensional maps: they are in fact following a great circle (see below).

Having defined a metric for the sphere, we may choose some collection of points on it and create Voronoi diagrams, just as before. The diagram below takes major airports around the world as seeds and constructs a Voronoi diagram on the Earth's surface (which, of course, is nearly a sphere).

Voronoi diagrams also have a number of applications outside mathematics in settings where understanding distances from a fixed set of sources is important. They are used in modeling the spread of disease, the growth of forests, cell development, the distribution of minerals in the Earth's crust, and rainfall maps, among other things. They are a beautiful visual tool for comprehending the relative positions of points in a given space.


Thursday, December 29, 2016

2016 Season Summary

The 2016 Atlantic hurricane season had below-average activity, with a total of

16 cyclones attaining tropical depression status,
15 cyclones attaining tropical storm status,
7 cyclones attaining hurricane status, and
3 cyclones attaining major hurricane status.

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

14 cyclones attaining tropical depression status,
13 cyclones attaining tropical storm status,
7 cyclones attaining hurricane status, and
3 cyclones attaining major hurricane status.

The season was just a bit above average, since the average numbers of tropical storms, hurricanes, and major hurricanes are 12.1, 6.4, and 2.7, respectively. My predictions at the beginning of the season were close to the actual result, with the only difference being in the number of tropical depressions and tropical storms. The Accumulated Cyclone Energy of the 2016 season was 132, an above average value, since there were a few relatively long-lived and intense hurricanes. In particular, Hurricane Matthew had an individual ACE of about 48, the highest for a single Atlantic hurricane in a dozen years.

The biggest story in 2015 for Atlantic hurricane development was the 2014-5 strong El Nino event. Indicated by anomalously warm ocean temperatures over the equatorial East Pacific region, this event limited the 2015 season to below-average activity. However, by the end of that year, it was diminishing, and fairly neutral conditions prevailed throughout the 2016 hurricane season. Generally speaking, El Nino inhibits tropical cyclone formation and La Nina conditions (with anomalously cool ocean temperatures over the same Pacific region) support it. The near-average 2016 season was consistent with this general rule.

Atlantic ocean temperatures were also not quite as extremely warm as in 2015, but more favorable atmospheric conditions in the Caribbean Sea and Gulf of Mexico allowed systems to form in areas likely to result in landfalls. Hurricane Matthew was by far the most notable hurricane of the season, strengthening into a category 5 in the Caribbean at an unprecedentedly low latitude. It was also the first category 5 in the basin since 2007. The system went on to devastate Haiti with a category 4 landfall, and later affected Cuba, the Bahamas, and the southeastern United States. Some other notable facts and statistics concerning this season include:
  • Hurricane Alex formed in January, making it the first hurricane to form in the month since 1938
  • Following the rapid start to the season with Alex and Bonnie, Tropical Storm Colin and Tropical Storm Danielle became the earliest forming 3rd and 4th tropical storms in an Atlantic season in recorded history
  • Tropical Storm Julia actually formed with its center of circulation over land, marking the first occurrence of this phenomenon since 1988
  • When Hurricane Nicole achieved category 4 status, 2016 became the first known season to have two category 4 hurricanes (the other was Matthew) exist in the month of October
  • The season ended on another unusual note, with Hurricane Otto becoming the southernmost landfalling hurricane in Central America ever recorded, and the first Atlantic storm to cross into the East Pacific basin since 1996
  • Unfortunately, the death toll of the 2016 season exceeded 1700 people (with most of these occurring in Haiti due to Hurricane Matthew), making 2016 the deadliest Atlantic hurricane season since 2005

The 2016 season was not extraordinarily active, but saw a relatively high number of landfalling systems in the Caribbean, the Gulf, and elsewhere.


Monday, November 21, 2016

Hurricane Otto (2016)

Storm Active: November 21-26

On November 12, a trough of low pressure making its way across the Caribbean stalled in the southwestern part of the sea north of Panama. The system organized very gradually without moving significantly over a period of many days. Thunderstorm activity increased on the 14th, leading to the formation of a low pressure the next day. The low drifted toward the coastline of Central America, halted, and reversed direction over the following couple of days, while conditions became less favorable and disorganized the system. However, it was still over the same region of warm waters on November 19 when conditions began to improve and the circulation became better defined. On November 20, the low deepened and was better defined still, but thunderstorm activity remained too weak for a tropical cyclone classification. Finally, early on November 21, Tropical Depression Sixteen formed in the southwestern Caribbean.

Located over warm ocean waters and surrounded by an environment of diminishing upper-level winds, the cyclone steadily strengthened. That afternoon, it was upgraded to Tropical Storm Otto. Otto was meanwhile trapped in an area of very weak steering currents and barely moved that day, managing only a slow southward drift. But while the system was nearly stationary, its structure improved considerably: strong thunderstorm activity increased and large curved banding features formed overnight. By midmorning of November 22, Otto was close to hurricane strength and its southern quadrant was bringing heavy rains to the northern coast of Panama. A little more intensification that afternoon resulted in Otto becoming a category 1 hurricane, breaking the record for latest hurricane formation in the Caribbean Sea set by Martha in 1969. Meanwhile, the system began to slowly move westward as a ridge established itself to the north.

The next day, wind shear and dry air weakened Otto slightly back to a tropical storm. This setback was temporary, however, as atmospheric moisture was increasing, and a large burst of intense convection that evening restored hurricane strength. Otto was also moving more steadily westward toward the Central American coast by this time as the ridge amplified. Tropical storm conditions began to affect southeastern Nicaragua and northeastern Costa Rica by the early morning hours of November 24. Around the same time, Otto quickly developed an eye feature and intensified into a Category 2 hurricane, reaching its peak intensity with 110 mph winds and a central pressure of 975 mb. With this intensification, Otto became the latest forming category 2 hurricane on record in the Atlantic basin. A few hours later, around 1 pm EST, Otto made landfall just north of the border of Nicaragua and Costa Rica. This was also the southernmost hurricane landfall in Central America on record. As a result, the storm affected some areas less prepared for landfalling hurricanes.

Soon, however, land interaction began to quickly weaken Otto. By the evening of the 24th it had weakened to a tropical storm. The weakened system, now moving more quickly westward, emerged into the East Pacific basin overnight. The Pacific waters were fairly warm, but Otto faced dry air and significant wind shear. It moved steadily just south of west and weakened until dissipation occurred on November 26.

The above image shows Hurricane Otto at category 2 intensity just before landfall.

Otto's track was unusual in many respects. In addition to becoming the southernmost landfalling Central America hurricane ever recorded, it was also the first cyclone to survive crossing from the Atlantic to the Pacific since 1996.

Wednesday, October 5, 2016

Hurricane Nicole (2016)

Storm Active: October 4-18

During late September, a tropical wave was traversing the central Atlantic. Strong upper-level winds made it difficult for the system to organize, but by October 1, a low pressure center developed and the disturbance was producing strong winds. It moved northwest over the following few days and slowly organized as conditions became somewhat more favorable. By October 3, thunderstorm activity had become more concentrated. The next day, the system was producing winds to tropical storm force, and the circulation became better defined. Therefore, the system was designated Tropical Storm Nicole late in the morning on October 4.

It exhibited organized banding features and a well-defined circulation through the next day despite moderate shear. Meanwhile, the small system moved generally west-northwest into October 5. The cyclone continued to defy somewhat unfavorable atmospheric conditions and rapidly intensified over the following day, achieving hurricane status during the afternoon of October 6. An eye appeared on satellite imagery at the same time, and Nicole sped to an intensity of 105 mph winds and a pressure of 968 mb. The cyclone then stopped in its tracks and reversed course toward the south by October 7. Wind shear increased drastically and weakened Nicole as quickly as it had strengthened in addition to periodically exposing the center. By October 8, the system was again a fairly weak tropical storm, though vigorous convection bursts appeared intermittently throughout the day.

Nicole once again slowed to a standstill overnight and upper-level winds slowly relaxed. This allowed the system to recover some organization and initiate a slow strengthening trend. Later on October 9, Nicole finally assumed a more typical northward motion after meandering over the open Atlantic for several days. The next day, the system was again a strong tropical storm. However, the system still struggled with some dry air aloft even as it passed over very warm waters. It managed to develop a ragged eye feature during the morning of October 11, and intensification restarted. In fact, the system rapidly intensified into a hurricane that evening, and a category 2 storm by early on October 12. By this point, the cyclone was moving north-northwestward toward Bermuda. Later that day, the eye became quite large and symmetric and the system had outstanding outflow in all quadrants. These new increases in organization merited an upgrade to a major hurricane that evening and Nicole reached category 4 status briefly that night. Its peak intensity of 130 mph winds and a minimum pressure of 950 mb occurred as the system accelerated toward the north and tropical storm force winds began to engulf Bermuda.

Just after achieving peak intensity, the cyclone experienced a huge increase in wind shear, causing significant weakening to begin early on October 13. Nicole's center passed within 10 miles of Bermuda that morning with the cyclone still at category 3 strength, bringing hurricane force sustained winds to the island. By this time, the system was turning toward the northeast and gaining forward speed. Meanwhile, shear and decreasing ocean temperatures quickly weakened Nicole back to category 1 strength. The system acquired some extratropical characteristics the next day, but rather than transitioning fully, it became a sort of hybrid cyclone: the windfield and size of the system were typical of an extratropical system, but the inner core remained that of a tropical cyclone.

Late on October 14, Nicole briefly weakened to a tropical storm, but baroclinic processes reintensified the system the next day to a very powerful north Atlantic hurricane. It also turned toward the east on October 15 and slowed in forward speed. By the next morning, it had maximum winds of 85 mph and a pressure of 958 mb and was generating large ocean swells throughout the north Atlantic. Some weakening ensued the following day, but Nicole remained a hurricane through the morning of October 17. Diminishing ocean temperatures finally caught up to the system that night, purging the remaining tropical characteristics, and Nicole became post-tropical early on October 18. The cyclone remained extremely powerful for the next few days as it interacted with a frontal low and brought unusually strong winds to the southern coast of Greenland before being absorbed.

The above image shows hurricane Nicole at peak intensity shortly before impacting Bermuda. Since Matthew and Nicole both were category 4 hurricanes in October, the 2016 season was the first in recorded history to have two storms of at least category 4 strength in this month.

Nicole's meandering track brought it southward before doubling back toward Bermuda, stalling over the far northern Atlantic, and finally having impacts as far north as Greenland as an extratropical system.

Thursday, September 29, 2016

Hurricane Matthew (2016)

Storm Active: September 28-October 9

On September 22, a tropical wave exited in the African coast and moved rapidly westward across the Atlantic. For the next few days, the wave remained south of 10°N and embedded in the Intertropical Convergence Zone. Combined with the dry air over the east Atlantic, this factor precluded development initially. By the 26th, thunderstorm activity had increased and spiral bands had begun to appear on the north side of the disturbance. The system was still too far south to acquire spin, but it began to move west-northwest over the following day and acquired additional organization. By September 27, the wave was generating winds to near tropical storm force, but had not yet developed a closed circulation. Early on September 28, the system appeared on satellite imagery to be more organized, and aircraft reconnaissance confirmed the presence of a closed circulation later that day. Therefore, advisories were initiated on Tropical Storm Matthew. The aircraft also estimated that surface winds of 60 mph were already present, making the newly formed Matthew already a strong tropical storm.

At the time of formation, Matthew was passing through the Lesser Antilles and entering the Caribbean, bringing strong storms to the region. During the morning of September 29, moderate shear out of the southwest exposed the center briefly. However, high ocean temperatures and increasing humid air near the system allowed an inner core to quickly develop. By the middle of the afternoon, Matthew had strengthened to a hurricane. Meanwhile, the cyclone veered slightly south of west. Overnight, strengthening continued, bringing Matthew to category 2 status by the morning of September 30. Conditions began to deteriorate in the northernmost areas of Columbia later that morning. It is very unusual for tropical cyclones to affect South America, but Matthew's track was quite far south through the Caribbean. Around the same time, an eye appeared on satellite imagery and further rapid intensification took place. That afternoon, the system vaulted through category 3 and up to category 4 status. During the late evening, Matthew peaked as a category 5 hurricane with winds of 160 mph and a central pressure of 941 mb, making it the first category 5 hurricane in the Atlantic since Felix in 2007. Achieving this intensity at 13.3°N latitude, it was also the southernmost category 5 hurricane ever recorded in the Atlantic.

The forward speed of the system had slowed considerably at this point, although it was still moving west or just south of west. Early on October 1, the eye shrunk and the inner core became less organized, resulting in some weakening that day. This weakening was temporary, however, for after completing a small cyclonic loop that afternoon, Matthew regained strong category 4 strength and its new lowest pressure of 940 mb. The cyclone's motion remained slow and somewhat erratic through the following day, averaging to a general northwestward track during the day of October 2. Later that day, the outer rain bands of Matthew began to affect Jamaica and Haiti as it approached from the south. The system turned to the north and experienced slight weakening that night, but still maintained category 4 intensity. Matthew's structure did not change much the next day as it steadily approached the Greater Antilles. Extremely heavy rains began over Haiti on the 3rd and continued as the storm came closer and closer. Early on October 4, the center passed well to the east of Jamaica, though the island still experienced tropical storm conditions. Meanwhile, Matthew's pressure dropped to 934 mb, though the winds remained within category 4 intensity. Around 7:00 am EDT on October 4, Matthew made landfall in southwestern Haiti with maximum winds of 145 mph, the strongest hurricane to make landfall in the country in over 50 years.

Interaction with land began to slowly weaken the system, though the inner core remained largely intact. The cyclone emerged over water a few hours later and traversed the channel between Cuba and Haiti that day. It remained a category 4 with 140 mph winds when it made landfall near the eastern tip of Cuba at 8:00 pm EDT that evening. The cyclone stalled its northward motion slightly over land and weakened more substantially, becoming a category 3 storm early on October 5. By that time, it had again emerged over water and was entering the Bahamas. An amplifying ridge to the cyclone's east caused a northwest turn later that day. Meanwhile, Matthew began to recover from its land interactions that evening, with the pressure dropping and winds increasing as the eye passed through the Bahamas. Later on October 6, Matthew peaked as a category 4 once again. Rain bands had begun to affect Florida's east coast at this point and the cyclone continued to move closer to land, turning toward the north as it did so. Overnight, the center moved roughly parallel to the central and northern Florida coastline, with the outer eyewall bringing strong winds and heavy rains to the coastline from about 30 miles offshore.

Land interaction and increasing shear also started to weaken the storm as it moved northward. By the time it passed the coast of Georgia very early on October 8, the winds had diminished to category 2 strength. Matthew continued its turn and began to move northeast parallel to the U.S. coastline before finally crossing the shore late that morning as a category 1 hurricane in central South Carolina. Though the maximum winds had decreased by this point, very high levels of moisture in the atmosphere contributed to a huge rainfall event for the Carolina coasts, with over 10 inches of rain falling over a large swath of the region. In addition, the cyclone produced a large storm surge that inundated some low-lying areas. However, by this point, the hurricane was quickly acquiring extratropical characteristics, and transition was completed early on October 9. Though the system was moving eastward away from the coast, rains continued in the Outer Banks of North Carolina through the day before tapering off. The extratropical system was absorbed by a front the next day.

Hurricane Matthew was the first category 5 hurricane in the Atlantic in 9 years. The storm killed over 1000 people, a majority of whom lived in Haiti, making it the deadliest cyclone in the Atlantic since 2005. It also caused over five billion dollars in damages and was the costliest Atlantic hurricane since Hurricane Sandy of 2012. The above image shows the cyclone at peak intensity in the Caribbean Sea.

Matthew formed and strengthened unusually far south in the Caribbean before turning sharply northward and impacting the Greater Antilles, the Bahamas, and the U.S. east coast.

Tuesday, September 20, 2016

Tropical Storm Lisa (2016)

Storm Active: September 19-24

On September 16, a tropical wave moved off of Africa into quite favorable conditions in the eastern Atlantic. As a result, an area of low pressure developed almost immediately and an impressively broad circulation developed. After initially having some trouble consolidating, the circulation became well-defined on September 19 and the system was classified Tropical Depression Thirteen. Shortly after formation, the depression took a west-northwest turn toward a weakness in the ridge to its north. Steady organization followed over the next 24 hours as the system strengthened into Tropical Storm Lisa during the morning of September 20 and then experienced more strengthening through that evening.

Due to the presence of an upper-level low pressure system located to the northwest of Lisa, shear out of the west and southwest began to increase dramatically on September 21, gradually exposing the center of circulation as convection retreated to the east. Lisa held its own, however, continuing to produce very deep convective bursts. It even rebounded from a momentary weakening that day by strengthening to its peak intensity of 50 mph winds and a pressure of 999 mb during the morning of September 22. There was evidence by this point that the circulation was becoming elongated in response to the continued shear. Meanwhile, thunderstorm activity began to wane and Lisa weakened through the rest of the day and overnight.

The storm experienced once last resurgence of thunderstorms during the morning of the 24th and in fact was upgraded back to tropical storm status as a result. However, this was only a temporary reprieve. By that afternoon, the circulation was entirely bare. Lisa was downgraded to a tropical depression that afternoon and a remnant low that night. The circulation produced shower activity for an additional few days before dissipation.

The image shows a disorganized Lisa over the eastern Atlantic.

A break in the ridge to Lisa's north allowed it to veer north quite far east and encounter hostile atmospheric conditions quite quickly.