Sunday, September 17, 2017

Hurricane Maria (2017)

Storm Active: September 16-

Maria formed from a tropical wave that first left Africa around September 10 or 11. At first, conditions did not support development of the broad system, but they steadily improved over the next several days. On September 15, the disturbance appeared much more organized on satellite imagery, and some rotation became evident. By the morning of the 16th, only a well-defined center of circulation separated it from tropical cyclone status. It cleared this hurdle during the afternoon, becoming Tropical Depression Fifteen. From this point, its maximum winds increased almost immediately, and the depression was upgraded to Tropical Storm Maria shortly thereafter.

The tropical storm was already quite large, though gaps remained in the satellite presentation of the cyclone in between rain bands. Despite this, the inner core strengthened fairly swiftly, and Maria became a strong tropical storm by the morning of September 17. That afternoon, a large burst of convective activity ignited near the center of circulation, overcoming the dry slot that had been hampering intensification. Soon, Maria had a well-formed eyewall and was upgraded to a hurricane. The outer bands were starting to affect the Lesser Antilles and the system continued west-northwestward toward the islands. September 18 saw incredibly rapid strengthening of Maria. In the morning, it strengthened into a major hurricane, and while an eye was apparent on radar, it had not yet cleared out on satellite imagery. The clearing came that afternoon; a very small "pinhole" eye developed, indicating a small core but extremely intense winds. Its intensity shot up through category 4, and Maria achieved category 5 intensity with 160 mph winds and a pressure of 924 mb during that evening. The eye then made landfall small island of Dominica in the Lesser Antilles.

Though small, the island was mountainous, and briefly disrupted Maria's core, bringing the intensity down slightly to category 4. However, as moved west-northwest into the Caribbean, its central pressure began to drop again, and the hurricane regained category 5 status early in the morning of September 19. Remarkably, the cyclone was not done intensifying: it became more symmetric on satellite imagery that day, and thunderstorm activity around the centered grew even further. That evening, Maria reached a peak intensity of 175 mph winds and a central pressure of 909 mb, one of the top ten lowest pressures ever recorded in an Atlantic hurricane at the time, even though its maximum winds were slightly weaker than those of Hurricane Irma a few weeks earlier.

By this time, the center was approaching Puerto Rico and the U.S. Virgin Islands. As is typical with powerful hurricanes, a secondary eyewall then formed and the inner one weakened somewhat, causing a decrease in maximum winds. When Maria made landfall in Puerto Rico early on September 20, it was a high-end category 4 hurricane with maximum winds of 155 mph, but the area of maximum winds had expanded in the wake of the eyewall replacement. Regardless, it was the strongest cyclone to make landfall in Puerto Rico since 1928. The hurricane brought extremely strong winds and damaging flooding rains to the island, causing several rivers to exceed their previous record stages. Nevertheless, land interaction took a significant toll on Maria and it quickly weakened over the next several hours. After traversing much of Puerto Rico from east-southeast to west-northwest, the center emerged over water early in the afternoon. The system had dropped to high-end category 2 strength, but reorganization began as it moved further northwest. A ragged eye developed by the evening and the circulation recovered some overnight, bringing Maria back up to major hurricane strength early on September 21. The southern portion of the circulation brought widespread tropical storm conditions and occasional hurricane conditions to the Dominican Republic that day.

As of 8:00 am EDT on September 21, 2017, Tropical Storm Maria had winds of 115 mph, and central pressure of 959 mb, and was moving toward the northwest at 9 mph. Please see the National Hurricane Center for current information, watches, and warnings.

Friday, September 15, 2017

Tropical Storm Lee (2017)

Storm Active: September 14-18

As is typical during mid-September, a strong tropical wave moved off of Africa and showed signs of organization by the morning of September 14. It was a fairly low-latitude system, passing well south of the Cape Verde Islands. The disturbance developed rather quickly, becoming Tropical Depression Fourteen that same night. After this, however, the system became a bit less organized, with the center becoming exposed to the north of the cloud canopy on September 15. However, as the system moved toward the west, it stayed south of the worst shear, and was able to slowly consolidate. Much more deep convection appeared during the morning of September 16, and the depression was upgraded to Tropical Storm Lee.

The system could not progress much further in its development, however, as upper-level winds renewed their assault from the north and west. The center once again became exposed later in the day, and the circulation was nearly devoid of thunderstorm activity by early on September 17. This caused Lee to weaken to a tropical depression. Pulses of convection intermittently covered the center over the next day but each was sheared away in turn. This allowed the storm to maintain tropical depression status as it turned west-northwestward. Even this did not last, however. Late on September 18, Lee lost even more organization and degenerated into a remnant low, far away from land.

Wednesday, September 6, 2017

Hurricane Katia (2017)

Storm Active: September 5-9

An area of low pressure formed in the Bay of Campeche on September 1. At first, strong shear prevented the system from doing more than generating shower activity over the region as it moved little. Conditions gradually improved for development, however, and by September 4, the disturbance was producing a large and concentrated area of thunderstorms over water. The next day, Tropical Depression Thirteen formed. There was very little steering the system, so it initially drifted toward the east and then east-southeast overnight. The system strengthened into Tropical Storm Katia early in the morning of September 5.

Later that day, the system developed a very compact inner core, and maximum winds increased rapidly. Just 12 hours after becoming a tropical storm, Katia was already a hurricane. When Katia became a hurricane, Irma and Jose were also hurricanes, making 2017 the first Atlantic season to feature 3 simultaneous hurricanes since 2010. Meanwhile, the system became nearly stationary during the morning of September 7. During the day, hints of an eye were seen, and Katia's winds increased gradually. A developing ridge to the hurricane's north finally set it on a definite heading overnight, this time toward the southwest. The next day, as it approached the coastline, the system reached its peak intensity as a category 2 hurricane with 105 mph winds and a minimum pressure of 972 mb. During the afternoon and evening, however, dry air invaded the circulation, and Katia collapsed weakening rapidly before even hitting land. By the time it made landfall in Mexico, it was down to minimal hurricane strength. The storm's swift demise continued, and it dissipated on September 9. The main impacts of Katia were heavy rain over the mountainous terrain of central Mexico.



The above image shows Katia at peak intensity as a category 2 hurricane. Fortunately, rapid weakening just before landfall reduced impacts in Mexico.



Weak steering currents prevailed during Katia's lifetime in the Bay of Campeche, and the system moved very slowly throughout its existence.

Hurricane Jose (2017)

Storm Active: September 5-

A new tropical wave entered the Atlantic basin right at the end of August and produced disorganized shower activity as it moved westward. Not much organization occurred until September 4, when conditions became more favorable and thunderstorm activity much more concentrated. By early on September 5, the disturbance was producing winds near tropical storm force. Hours later, the center of circulation was organized enough to name the system Tropical Storm Jose. The newly-formed storm was located about halfway between Africa and the Lesser Antilles and was moving west-northwest.

Moist air and low shear allowed Jose to begin strengthening immediately. A predecessor to an eye was already becoming evident during the afternoon of September 6, and the cyclone was a minimal hurricane by the evening. Simultaneously, Irma and Katia were also hurricanes, making 2017 the first Atlantic season to have three hurricanes at once since 2010. Jose's intensification continued well beyond category 1 strength. During the afternoon of September 7, it became another major hurricane as the eye became well-defined on satellite imagery. The next morning, it exploded into strong category 4 intensity. Jose's heading shifted northwest during the day, bringing on a track to just miss the northern Leeward Islands to the northeast. As it approached the islands during the evening, the storm reached its peak intensity of 155 mph winds and a central pressure of 938 mb, just below category 5 strength.

Partially due to the outflow of Irma, upper-level winds became less favorable for Jose overnight, and a weakening trend had begun by the morning of September 9. The hurricane made its closest approach to the northern Leeward Islands before noon. Fortunately for the islands, which had been devastated less than four days prior by Hurricane Irma, the center passed to the northeast, and wind radii were low on the southwest side. Nevertheless, tropical storm conditions did affect some areas for the better part of the day. The system moved northwest away from the Caribbean that evening, and Jose maintained category 4 strength through the morning of September 10. The eye disappeared that day, however, and the system steadily fell through category 3 strength into category 2 overnight. Very deep convection was still present around the center, however. Atmospheric steering currents were also weakening, causing Jose to lose forward speed and veer toward the north into September 11. During the day a developing mid-level ridge began turning the system toward the east, and its heading was due east by early the next morning. Although the hurricane maintained impressive thunderstorm activity during this time, little to no banding could form in the face of strong wind shear. As a result, Jose decayed into a minimal category 1 hurricane by September 12.

At this point, the system stabilized in intensity, and continued its slow clockwise loop over the western Atlantic by moving southeast overnight and into September 13. Warm waters allowed large pulses of deep convection to continue, offsetting the unfavorable upper-level winds and causing some upward fluctuations in intensity. Later that day, Jose turned sharply south and then west as the nearby ridge continued to evolve. The system lost some organization overnight, and weakened a bit on September 14 to a tropical storm. Another factor that inhibited strengthening later that day and early the next is that Jose was completing its loop and crossing over cooler ocean waters left in its wake when it traveled across the region a few days previously. Nevertheless, the storm remained at the brink of hurricane strength into September 15. That day, it recovered some deep convection as it turned northwest, and restrengthened into a hurricane. The storm still struggled some with dry air over the next day, but gradual strengthening occurred. Having reached the western periphery of the steering ridge, Jose also took an overall turn toward the north, although the center wobbled some to the east and west as it did so. On September 17, Jose reached its secondary peak strength of 90 mph winds and a pressure of 967 mb.

By that evening, Jose was beginning to display some characteristics of an extratropical cyclone. As it passed the latitude of North Carolina well offshore, its inner core weakened but its wind field expanded. Nevertheless, it hung on to minimal hurricane strength over the next day as it continued generally northward. Early on September 19, the cyclone's outermost rain bands swept across the mid-Atlantic coast and southern New England. Later in the day, the system turned toward the northeast, away from the coast, though the system was so large that some coastal rains continued. By this time, the center of circulation had moved north of the warm Gulf Stream waters, resulting in weakening. Jose finally lost hurricane status and became a tropical storm. Gradual decay continued into September 20. Meanwhile, the storm turned toward the east and slowed down, coming nearly to a standstill that night southeast of Cape Cod. Rain continued for portions of southern New England through the 21st.

As of 8:00 am EDT on September 21, 2017, Tropical Storm Jose had maximum winds of 60 mph, a minimum central pressure of 982 mb, and was nearly stationary. Please see the National Hurricane Center for current information, watches, and warnings.

Wednesday, August 30, 2017

Hurricane Irma (2017)

Storm Active: August 30-September 12

On August 28, another vigorous tropical wave emerged off of the coast of Africa. Saharan dry air did not hamper it as it had its predecessors, and the wave maintained thunderstorm activity as it passed near the Cape Verde Islands on August 29, bringing locally heavy rain and gusty winds. Before long, its circulation became better-defined and it developed gale-force winds. As a result, advisories were initiated on Tropical Storm Irma during the morning of August 30. Already, the storm had 50 mph sustained winds, and strengthening continued steadily as Irma's inner core became better defined. The system turned a bit toward the west-northwest on August 31, and an eye feature suddenly appeared on satellite imagery. Irma was undergoing extremely rapid intensification, and was upgraded directly from a tropical storm to a category 2 hurricane and then a major hurricane by late afternoon.

The circulation was quite compact, with hurricane-force winds very close to the center. As is often true with small cyclones, Irma was subject to short-term fluctuations in intensity. A few eyewall replacement cycles, in which the eye clouded over temporarily and then reappeared, occurred between August 31 and September 2. This caused Irma to alternate between category 2 and category 3, an impressive intensity as it traversed only marginally warm waters. Meanwhile, the subtropical ridge to its north began to build southward, and the cyclone turned west and even slightly south of west by September 2. Over time, this brought the system toward warmer waters and moister air. By September 3, though Irma's intensity remained in the low-end category 3 range, the cyclone was beginning to grow larger, displaying outer banding features. That evening, Irma's central pressure began to decrease. This trend continued into September 4, when the maximum winds began to strengthen as well.

Meanwhile, Irma began to round the bottom of the subtropical ridge and assume a due westward path near 17° N. This brought it over areas of higher oceanic heat content and even higher atmospheric humidity levels. As a result, intensification once again increased in speed: Irma became a category 4 that afternoon. During the evening, its eye cleared and became quite large in the wake of another eyewall replacement. During the morning of September 5, yet another burst of intensification brought it to category 5 strength, with winds of 175 mph. This was the farthest east such high wind speeds had ever been recorded in the Atlantic. The outer part of Irma's circulation began to affect the northeast Caribbean islands that day. The trend of remarkable deepening continued as the system turned west-northwest, bringing the hurricane to a peak intensity of 185 mph winds and a minimum pressure of 914 mb. These winds were tied for the second-highest ever recorded in an Atlantic hurricane, and the pressure was the lowest known in the Atlantic outside of the Caribbean and Gulf of Mexico. That night, the cyclone passed directly over the northern Leeward Islands.

Despite the continuing evolution of the inner core, Irma did not undergo an eyewall replacement on September 6, and maintained its incredible category 5 intensity, though with some pressure fluctuations. The center passed through the U.S. Virgin Islands and then just north of Puerto Rico that evening. Overnight, the circulation was a bit disrupted from land interaction, and the winds began to slowly decrease as Irma moved west-northwest just north of Hispaniola. That evening, the center of circulation passed among the Turks and Caicos Islands. During the night, the outer eyewall of Irma finally got the better of the inner, weakening the maximum winds down to category 4 strength, but expanding the overall windfield. The system moved west-northwest between Cuba and the Bahamas the morning of the 8th as a strong category 4 hurricane. Late in the afternoon, Irma turned back toward the west and approached the northern coast of central Cuba. Just before making a direct hit on the northern archipelago of Cuba, the system briefly regained category 5 strength, reaching winds of 160 mph and a minimum pressure of 924 mb.

After passing over the northern islands, the center of circulation did not pass inland, but rather turned just north of west and paralleled the coast overnight, slowing down as it did so. Land interaction took a significant toll on the storm for the first time early on September 9, dropping Irma down to high-end category 3 strength. The eye wobbled a great deal along its path during the day, but the overall motion was a turn toward the north-northwest by the evening. Meanwhile, as conditions improved in Cuba, they deteriorated in Florida, as intense outer bands swept across much of the peninsula. These include tropical storm conditions, flooding rains, and several reports of tornadoes. During the night, Irma regained category 4 intensity, reaching a final peak of 130 mph winds and a pressure of 928 mb before passing over the Florida Keys early on September 10. Increasing wind shear and land interaction steadily weakened Irma from then on. It made landfall as a category 3 hurricane in southwestern Florida that afternoon. As with many sheared landfalling systems, Irma became lopsided, with almost all rainfall occurring north of the center, and the northern eyewall much more intense than the southern. The size of the system was such that, located over western Florida, it brought tropical storm force winds from the Florida panhandle to parts of Georgia and even extending well into South Carolina.

On September 11, Irma weakened to a tropical storm while centered over the northwestern Florida Peninsula, having caused more than 6 inches of rain throughout much of the state. By the afternoon, the center had pushed into Georgia and rains spread northwestward as they ended in Florida. Overnight, the system weakened to a tropical depression and then became post-tropical. In addition to those already mentioned, Irma set many other records. Its 3.25 days spent as a category 5 hurricane were tied for the most ever recorded in the Atlantic with the 1932 Cuba hurricane. Its category 5 landfalls in the Leeward Islands and Cuba were among the strongest ever recorded. Finally, Irma maintained 185 mph winds for a period of 37 hours, which was the most ever recorded in the entire world.



This image shows Hurricane Irma at peak intensity on September 6 as it passed directly over the northern Leeward Islands, causing catastrophic damage.



Irma's long track as a powerful hurricane brought devastating impacts to the northern Leeward Islands, the U.S. Virgin Islands, the Turks and Caicos Islands, Cuba, and Florida.

Thursday, August 17, 2017

Hurricane Harvey (2017)

Storm Active: August 17-19, 23-31

On August 13, a large tropical wave entered the Atlantic from the west coast of Africa. As with many of the previous August waves, thunderstorm activity diminished as soon as it was over water. There was some spin associated with the system over the next few days, but the low pressure area remained elongated. The circulation improved greatly on August 15 and 16, leaving limited shower activity as its main barrier to development. Meanwhile, the system was moving due westward at a steady clip toward moister air, and thunderstorm activity increased significantly by the morning of the 17th. That afternoon, aircraft reconnaissance discovered a closed circulation and tropical storm force winds, prompting the naming of Tropical Storm Harvey.

After formation, Harvey moved at around 20 mph toward the west, steered by a ridge to its north. As with many systems moving at such speeds near the Lesser Antilles, the storm had difficulty maintaining a center of circulation and was rather disorganized. Nevertheless, it brought some localized heavy rain and gusty winds as it passed over the Windward Islands during the morning of August 18. Moderate shear also took a toll on the system as it continued quickly westward; during the afternoon of August 19, it was downgraded to a tropical depression. The system's deterioration continued through the evening and aircraft reconnaissance was unable to detect evidence of a closed circulation that evening. Harvey had opened up into a wave and was no longer a tropical cyclone.

The remnants of Harvey continued toward the west, where conditions for development began to improve again. Early on August 20, they passed near the coasts of Nicaragua and Honduras, bringing some rain to the shoreline. Shower activity increased significantly that afternoon. Before a new circulation could fully develop, however, the system began to interact with the Yucatan Peninsula. While Ex-Harvey crossed over land on August 21 and 22, it produced convection mainly over the Gulf waters to the north. Nevertheless, some spin reappeared on satellite imagery. The system became much more vigorous by the morning of the 23rd, once it was back out over warm Gulf waters. Aircraft reconnaissance soon found a well-defined center of circulation and advisories were reinitiated on Tropical Depression Harvey before noon.

During the afternoon, Harvey slowed to a standstill, and a central dense overcast feature appeared, indicative of a developing system. The central pressure began to slowly decline, but the circulation was still rather disorganized. Overnight, the depression was upgraded to a tropical storm. The upper-level low that was causing some shear over Harvey was weakening, meanwhile, leaving the storm in very favorable atmospheric conditions. Early on August 24, the system began a run of rapid intensification, reaching hurricane strength by early in the afternoon! Though the wind speeds leveled out through the evening, the central pressure continued to drop, presaging a corresponding increase of winds. This occurred in the middle of the night, bringing Harvey to category 2 strength. Around this time, a vigorous outer rain band swept across the Texas coastline. During the morning of August 25, it became evident that the hurricane was experiencing an eyewall replacement cycle (EWRC), where the innermost ring of thunderstorms about a powerful hurricane's eye contracts or dissipates, and a second ring (the outer eyewall) takes over. This put a temporary cap on Harvey's winds, but did not stop the central pressure from dropping steadily.

Meanwhile, the system was still moving at a moderate pace toward the northwest and approaching the Texas coastline. Squalls and even tornadoes occurred over land as the more vigorous rain bands swept across the coast. During the afternoon, Harvey's EWRC was completed, and a large eye cleared out on satellite and radar imagery. This was accompanied by another rapid increase in winds, bringing the hurricane to its peak intensity as a category 4 storm; it had maximum winds of 130 mph and a central pressure of 938 mb when it made landfall in Texas. This was first major hurricane landfall in the United States since 2005, the first hurricane landfall in Texas since 2008, and the strongest in the state since 1961. The storm slowed as it moved north-northwestward inland and weakened. By mid-morning on August 26, Harvey was a minimal hurricane, and it weakened to a tropical storm that afternoon. However, as the storm slowed to a standstill, the greatest concern was rain: the counterclockwise spin of the circulation continually brought new moisture from over the Gulf northward over areas east of the center, dumping feet of rain over a wide swath of Texas. Harvey reversed course and began to meander generally southward by the morning of August 27. Later, the direction of drift turned southeastward. Since part of the circulation remained over water, the storm was able to maintain minimal tropical storm strength through the next day. Meanwhile, the main source of rain was a large band wrapping around the northeast side of the circulation down to the Gulf, pulling moisture over eastern Texas and Louisiana. Early on August 28, Harvey's center reemerged over the Gulf of Mexico.

Some intermittent convection rekindled near the center once it touched warm Gulf waters, but the circulation was entraining dry air from western Texas, and wind shear was high. As a result, the inner core could not redevelop, and Harvey resembled an extratropical cyclone more than a tropical one. It had a comma-shaped tail of thunderstorm activity wrapping from north of the center eastward, so that rain continued over eastern Texas and Louisiana. The cyclone traveled first southeast, and then east over the next day. Winds increased modestly during this period to 50 mph in strong rain bands over water. Finally, on the 29th, Harvey turned toward the north and increased in speed somewhat, making its final landfall in western Louisiana early on August 30. The cyclone weakened over land as it moved north, but dealt a final burst of heavy rain to eastern Texas before becoming a tropical depression that evening. Soon, the system became extratropical, but rainfall continued to push northeastward, bringing moderate amounts of rain to the mid-Atlantic and northeast by September 2. A peak rainfall accumulation of 51.88" occurred in Cedar Bayou, Texas, the highest rainfall total every recorded from any tropical cyclone in the continental United States.



The above image shows Harvey shortly before landfall in Texas.



Harvey's unusual slow movement near and over the state of Texas brought unprecedented rains to south and east parts of the state.

Sunday, August 13, 2017

Hurricane Gert (2017)

Storm Active: August 12-17

On August 2, a vigorous tropical wave left Africa and moved westward over the Atlantic Ocean. While environmental conditions seemed conducive for development, the system was unable to consolidate. Dry air interfered with the production of deep convection, and the associated circulation remained highly elongated. Competing vortices on the northeast and southwest sides vying for dominance cost the wave the chance to organize over the next several days. By August 7, conditions had become unfavorable due to the presence of an upper-level low to the northeast. Nevertheless, the system proceeded steadily west-northwestward, passing a bit north of the Lesser Antilles on August 10. Wind shear diminished and the wave encountered more humid air soon after, giving it another chance at development. Convection increased and the circulation became better defined over the next two days, and Tropical Depression Eight finally formed late on August 12.

The system was experiencing some wind shear out of the north, but conditions were otherwise supportive of intensification. August 13 saw the naming of Tropical Storm Gert when the system lay well east of the Florida coastline and was turning toward the north. The inner core structure improved considerably that night and into August 14. The first hints of an eye appeared that afternoon, and Gert was upgraded to a hurricane that night. The cyclone then began to feel the influence of a frontal system moving off of the U.S. east coast, and turned northeast on August 15, accelerating as it did so. Even as it gained latitude, Gert still took advantage of warm Gulf Stream waters to continue strengthening. A compact eye feature became apparent on both visible and satellite imagery by the morning of the 16th. That evening, the system reached its peak intensity as a category 2 hurricane with 105 mph winds and a minimum pressure of 967 mb near 40° N. Cooler waters and deteriorating atmospheric conditions finally caught up with Gert overnight and it weakened, beginning extratropical transition. The system became extratropical on the afternoon of August 17 as it sped east-northeastward over the open ocean.



The above satellite image shows Gert at peak intensity as a category 2 hurricane. Nova Scotia is visible at the top of the image.



A frontal boundary interacting with Gert steered it out to sea, minimizing land impacts.

Monday, August 7, 2017

Hurricane Franklin (2017)

Storm Active: August 6-10

Towards the end of July, a tropical wave tracked westward across the central Atlantic, showing some potential for development as it produced scattered showers and thunderstorms. Dry air and deteriorating atmospheric conditions stifled this potential by the time August had begun. Nevertheless, the tropical wave continued into the Caribbean. Significant convection flared up near the system on August 3 when it was located in the eastern Caribbean, and surface pressures began to slowly decline in the area. For the next day or two, however, it was contending with very high wind shear, and was unable to organize much. This changed early on August 5, when thunderstorm activity concentrated near its nascent circulation. Meanwhile, shear began to decline, allowing the system to take advantage of quite warm sea water. Late on August 6, Tropical Storm Franklin was named northeast of Honduras.

Franklin's environment steered it steadily west-northwest the following day. Its banding features steadily improved, resulting in steady strengthening. By that afternoon, its sustained winds had increased to 60 mph and its pressure had dropped to 999 mb. However, dry air infiltrated the circulation from the south that evening, weakening thunderstorm activity near the center and preventing additional intensification before Franklin made landfall that evening in the Yucatan Peninsula. The cyclone weakened over land into August 8, but the low-lying land did not disrupt the core much, and the system remained well-organized. Late in the afternoon, the center of circulation emerged over the Bay of Campeche and assumed a more westward trajectory. Strong outer bounds quickly formed and Franklin's core also quickly improved over the very warm ocean water. The following day saw the system intensify from a minimal tropical storm to a category 1 hurricane by the afternoon of August 9. It strengthened a bit further to its peak intensity of 85 mph winds and a pressure of 981 mb before making landfall in Mexico. Franklin's decay was swift over the mountainous terrain, and it dissipated by late morning on August 10.

The remnants of Franklin crossed over into the eastern Pacific Ocean over the next day and quickly reorganized over water. Late on August 11, they regenerated into a tropical storm. Since the system dissipated before reforming in another basin, it received a separate name from the Eastern Pacific name list: Jova.



The above image shows Hurricane Franklin at peak intensity just before landfall in Mexico.



Franklin strengthened quickly over the warm waters of the Bay of Campeche.

Monday, July 31, 2017

Tropical Storm Emily (2017)

Storm Active: July 31-August 1 During the last week of July, a cold front extending from Texas to the northeast U.S. pushed south and east, weakening as it did so. By July 30, the southern half of the cold front had moved over the Gulf of Mexico and stalled. A non-tropical low quickly formed along it just south of the Florida panhandle and moved slowly toward the east. Overnight, thunderstorm activity became clustered around the circulation center and the system became organized enough to merit tropical depression status early on July 31. Just two hours after formation, radar indicated that Tropical Depression Six's maximum winds had risen to 45 mph and it was upgraded to Tropical Storm Emily.

The storm moved just south of east through the morning and made landfall near Tampa, Florida before noon. Heavy rain fell even as the system weakened over land, with the heaviest south of the center. By the afternoon, the system had weakened to a depression. It accelerated and turned toward the northeast overnight and emerged over open Atlantic waters east of Florida early on August 1. Emily's grip on tropical cyclone status was quite tenuous by this time: only scattered bursts of disorganized convection remained. Late that night, it was downgraded to a remnant low. This low continued out to sea over the next several days before dissipation.



The above image shows Tropical Storm Emily making landfall in Florida within 12 hours of formation.



Emily was yet another short-lived tropical storm, the fifth of the 2017 season. In fact, the combined ACE (accumulated cyclone energy) of these storms was the lowest on record for the first five of an Atlantic hurricane season.

Monday, July 17, 2017

Tropical Storm Don (2017)

Storm Active: July 17-18

A mid-July tropical wave crossed westward from the coast of Africa to more than half-way across the tropical Atlantic without generating much thunderstorm activity. However, on July 16, the system began to organize, despite the proximity of dry air. A low pressure center formed shortly afterward, even as convection remained quite limited. During the afternoon of July 17, a curved band developed about the center and the circulation became better-defined. As a result, the low was upgraded to Tropical Storm Don about 500 miles east of the Windward Islands.

Over the next day, Don moved quickly toward the west. It strengthened briefly as a central dense overcast appeared, but increasing shear reversed this slight intensification as quickly as it had occurred. By midday on July 18, Don's disorganized thunderstorm activity was moving over the Windward Islands. That evening, before the system passed over the islands, Don lost its circulation center in the face of strong shear and dissipated. Scattered gale force winds and heavy rain did continue, however, as its remnants entered the Caribbean.



Tropical Storm Don was only a small cyclone for its brief existence, forming as it did on the edge of a dry air mass with limited moisture supply.



Don existed for less than two days before succumbing to high wind shear as it entered the Caribbean Sea.

Thursday, July 6, 2017

Tropical Depression Four (2017)

Storm Active: July 5-7

At the beginning of July, a tropical wave located southwest of the Cape Verde Islands began to organize. The system was moving rather slowly for its latitude over the next several days, allowing it to began circulating more easily than it otherwise would. Slowing development, however, was its interaction with the intertropical convergence zone (ITCZ). Even though this interaction generated a great deal of convection, the disturbance needed to separate from the ITCZ to initiate development. On July 4, the system began to veer toward the west-northwest and gain some latitude. The next day, it acquired a circular area of strong thunderstorms near its center and became Tropical Depression Four over the open tropical Atlantic.

Shortly afterward, however, the system began to feel the effects of a Saharan dry air encroaching from the north and east. On July 6, the depression continued to the west-northwest, but its thunderstorm activity slowly declined as it entrained dry air. In addition, the cyclone increased in forward speed, making it difficult for the circulation to persist. It did not persist long, in fact: the system lost a closed circulation and dissipated during the afternoon of July 7, far from any land.



The above image shows Tropical Depression Four over the open Atlantic.



The short-lived tropical depression fell victim to a large dry air mass quickly after formation.

Tuesday, June 20, 2017

Tropical Storm Cindy (2017)

Storm Active: June 20-22

On June 16, a large trough of low pressure formed over the western Caribbean Sea and the neighboring regions of central America. Heavy rainfall fell over adjacent landmasses as the system organized just east of the coast of Belize and moved slowly northward. By late on June 18, a huge north-south area of convection lay just to the east of the center of the disturbance, but it was still not organized enough to be considered a tropical cyclone. When it moved over the Gulf of Mexico shortly afterward, the open waters stimulated further development: finally, on June 20, it developed into Tropical Storm Cindy.

From its formation onward, Cindy did not look particularly like a tropical storm. The center remained largely devoid of convection, with several low-cloud swirls competing for dominance. Heavy rain was falling, but well away from the center in the northern semicircle. Much of this precipitation was already falling over land, from eastern Texas to the Florida panhandle. Cindy moved slowly toward the northwest as a medium-strength tropical storm through that night and June 21. Unfavorable wind shear prevented the storm from intensifying further. Early the next morning, Cindy made landfall near the border of Louisiana and Texas. After landfall, it quickly weakened to a tropical depression. The remnants of Cindy continued to bring rain over the U.S. as it traveled northeastward at a progressively faster clip over the following days.



Tropical Storm Cindy was a rather asymmetrical system with little to no convection near the center of circulation.



Cindy existed as a tropical cyclone only briefly in the Gulf of Mexico before making landfall.

Tropical Storm Bret (2017)

Storm Active: June 19-20

On June 13, a tropical wave formed just off the Atlantic coast of Africa and began rapidly moving toward the west. From the beginning, the system was located at a very low latitude, but was quite vigorous in its production of thunderstorm activity. Conditions were favorable for development in the low-latitude tropical Atlantic, and organization proceeded slowly over the next several days. By June 18, the wave had developed a broad circulation, but was having difficulty acquiring a well-defined center due to its rapid westward motion. The next day, a closed center was found; since gale force winds were already occurring north of the center, it was classified Tropical Storm Bret. At the time, it was centered just east of coastal Venezuela moving toward the west at a blustering 30 mph.

Early on June 20, the center of Bret crossed extreme northern Venezuela and moved into the much more hostile environment of the eastern Caribbean, where wind shear was quite high. The system's circulation, never well established, did not long survive these conditions, and Bret dissipated that same afternoon. Bret was the first known system to develop so early in the season within the low-latitude tropical Atlantic east of the Caribbean. It was also the lowest-latitude Atlantic tropical system in June since 1933.



The above image shows Tropical Storm Bret near the island of Trinidad.



Though short-lived, Bret was an unusual tropical storm. It was one of a rare class of tropical cyclones to make landfall in South America.

Monday, May 15, 2017

Professor Quibb's Picks – 2017

My personal prediction for the 2017 North Atlantic Hurricane season (written May 15, 2017) is as follows:

15 cyclones attaining tropical depression status*,
15 cyclones attaining tropical storm status*,
6 cyclones attaining hurricane status, and
3 cyclones attaining major hurricane status.
*Note: Tropical Storm Arlene formed on April 19, long before the official start of the season on June 1 and before I made these predictions.

This prediction calls for a nearly average Atlantic hurricane season, with predictions slightly exceeding historical averages in all categories.

In contrast to 2016, the conditions for the 2017 season are fairly common and uncertainty is relatively low. The first condition taken into account is the state of the El Niño Southern Oscillation Index (or ENSO index), a measure of sea surface temperature anomalies in the Pacific Ocean that has a tendency to affect Atlantic hurricane activity. After the index took a brief dip into negative territory this past winter, the index has returned to nearly zero, or "neutral." As shown in the figure below from the International Research Institute for Climate and Society, a modest increase is expected over the coming months.



As a result, the conditions prevailing for the hurricane season are likely to be neutral or weakly El Niño. Since El Niño tends to suppress Atlantic activity and cause cyclones to, on average, take more easterly tracks, this factor would suggest a quieter hurricane season.

Sea surface temperatures, meanwhile, are a bit above average across the Atlantic basin, but the anomalies are not as great in magnitude as they have been over the past few years. The warmest areas are currently the Caribbean and the tropical portion of the Atlantic farther east. Parts of the Gulf of Mexico, meanwhile, are slightly cooler than average. Further warming of the current higher-than-normal areas is likely over the next few months, so these might be conducive to cyclonogensis. The tropical Atlantic has also been quite moist, as has the Caribbean, supporting the development of hurricanes. The Gulf of Mexico, in contrast, has been persistently dry. Finally, with the developing El Niño, increasing wind shear is likely across the Atlantic, especially at higher latitudes and near the United States. Such shear is hostile to tropical systems, so I predict limited activity near the U.S. east coast, despite a pocket of warm water there.

My estimated risks for different parts of the Atlantic basin are as follows (with 1 indicating very low risk, 5 very high, and 3 average):

U.S. East Coast: 3
The presence of an El Niño would tend to reduce risk, as stated above. However, seasonal forecasts indicate that high temperatures will prevail near the coast for most of the summer, resulting in higher oceanic heat content. Look for quick forming and quick hitting systems - long-lived hurricanes are likely to miss the coast this year.

Yucatan Peninsula and Central America: 3
Signs in the adjacent Caribbean Sea point to elevated tropical activity this year: warm waters, moist air, and limited wind shear. However, steering ridges will have a difficult time setting up along the Caribbean Islands to the north, preventing developing storms from tracking due westward for the most part and instead allowing them to gain latitude. A combination of these two opposing factors leads to the "average" designation for this region.

Caribbean Islands: 4
Complementing the previous point, the Caribbean Islands will be in the more likely path of tropical cyclones. Coupled with the fact that the tropical Atlantic is warm, there is significant risk for landfalling tropical storms and hurricanes this year.

Gulf of Mexico: 1
Atmospheric conditions about the Gulf are already dry and strong upper-level winds are moving across the region. With an increasing ENSO index, this state of affairs is likely to continue indefinitely. Combined with the slightly cooler waters, these signs indicate a very low risk for the Gulf coast.

Overall, the 2017 season is expected to be near or just slightly above average, but with a lower than average risk to landmasses (most storms should curve out to sea). While the confidence in this forecast is somewhat higher than last year, everyone in hurricane-prone areas should still take due precautions as hurricane season approaches. Dangerous storms may still occur in quiet seasons. Sources: http://www.cpc.ncep.noaa.gov/products/analysis_monitoring/lanina/enso_evolution-status-fcsts-web.pdf, http://www.ssd.noaa.gov/PS/TROP/TCFP/atlantic.html

Saturday, May 13, 2017

Tropical Storm Arlene (2017)

Storm Active: April 19-21

During mid-April, a non-tropical low over the central Atlantic well east of Bermuda was producing a large area of tropical storm force winds and scattered thunderstorm activity. As the system drifted eastward, it more more organized, and began to show signs of subtropical development by April 18. Though convection remained mainly confined to the southeast quadrant by the next morning, the low had acquired enough organization to be classified Subtropical Depression One. At that time, the cyclone was moving north-northeast at a moderate clip as it interacted with an extratropical low.

Any cover the center of circulation had managed to develop that day was quickly stripped away by increasing wind shear by early on April 20. The system made a comeback later that morning, however, and in fact became more symmetric, resulting in its reclassification as a tropical depression. It turned toward west-northwest that afternoon and unexpectedly strengthened into Tropical Storm Arlene, only the second known tropical storm to form in April in the Atlantic. Further, its central pressure dropped to 993 mb, the lowest for a tropical system ever recorded in the month of April. Arlene's unusual run ended the next day as it became extratropical and was quickly absorbed by a larger system.



The above image shows Tropical Storm Arlene near its peak intensity over the open Atlantic.


Arlene did not approach any landmasses during its short lifetime. However, it was notable in that it was only the second Atlantic tropical storm known to form in April, after Ana in 2003.

Friday, May 12, 2017

Hurricane Names List – 2017

The name list for tropical cyclones forming the North Atlantic basin for the year 2017 is as follows:

Arlene
Bret
Cindy
Don
Emily
Franklin
Gert
Harvey
Irma
Jose
Katia
Lee
Maria
Nate
Ophelia
Philippe
Rina
Sean
Tammy
Vince
Whitney

This list is the same as used in the 2011 season, with the exception of Irma, which replaced the retired name Irene.

Sunday, April 16, 2017

OSIRIS-REx

OSIRIS-REx is a NASA sample return mission to the near-Earth asteroid 101955 Bennu. It aims to collect a sample from an asteroid whose composition could reveal a great deal about the beginning of the Solar System and the formation and evolution of the Earth. The first asteroid sample return mission was Hayabusa, developed by the Japanese Aerospace Exploration Agency (JAXA). This probe returned about 1,500 microscopic grains from the asteroid 25143 Itokawa. OSIRIS-REx, however, was designed to obtain at least 60 grams of material in the form of macroscopic samples. In addition, Bennu differs enormously from Itokawa in that it is carbonaceous while the latter is siliceous. Further, there is evidence that it is rich in organic and volatile compounds. Bennu is also of interest because its orbit takes it very close to Earth. It was measured to have a small cumulative probability of 0.037% of striking the Earth sometime in the 22nd century. This is due to the present uncertainty as to whether Bennu with pass through a gravitational "keyhole" in its 2135 flyby of Earth that would set it on a collision course. This mission will allow more precise predictions of its trajectory.



Bennu's orbit is slightly larger than Earth's but also more elliptical. As a result, it crosses inside Earth's orbit with every revolution.

The spacecrafts's name stands for Origins, Spectral Interpretation, Resource Identification, Security, Regolith Explorer. This unwieldy acronym contains the four main goals of the mission: to return a sample to Earth that will elucidate the Solar System's origins, to map the asteroid with spectroscopy to learn about its composition and formation, to investigate whether near-Earth asteroids such as Bennu could provide materials as resources for human development, and to discover what impact threat Bennu poses, if any. The word "regolith" describes the layer of loose material at the surface of an asteroid, from which OSIRIS-REx will obtain a sample.

On September 8, 2016, the OSIRIS-REx mission began with a launch from Cape Canaveral. After arriving at Bennu in 2018, it will map the surface to select a target for the 2019 sample acquisition. After leaving the asteroid in 2021, the spacecraft will then return the sample to Earth in 2023.

Sources: http://www.asteroidmission.org, http://www.space.com/33616-asteroid-bennu-will-not-destroy-earth.html, http://global.jaxa.jp/press/2010/11/20101116_hayabusa_e.html, http://science.nasa.gov/media/medialibrary/2012/05/04/OSIRIS-REx_--_Jason_Dworkin.pdf, http://science.nasa.gov/media/medialibrary/2012/05/04/OSIRIS-REx_--_Jason_Dworkin.pdf

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 Agnès 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.

Sources: https://arxiv.org/pdf/1601.05438v1.pdf, https://en.wikipedia.org/wiki/Argument_of_periapsis, http://arxiv.org/pdf/1602.06116v3.pdf, http://arxiv.org/pdf/1603.05712.pdf

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.

Sources: http://home.dtm.ciw.edu/users/sheppard/pub/TrujilloSheppard2014.pdf, http://www.aoi.com.au/bcw1/Cosmic/Sedna-PIA05569-sml.jpg

Sunday, February 12, 2017

Rainbows

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.

Sources: http://www.atoptics.co.uk/rainbows/primary.htm, http://www.physicsclassroom.com/class/refrn/Lesson-4/Rainbow-Formation, http://0.tqn.com/d/weather/1/S/j/T/-/-/water-drop-prism-lrg_nasascijinks.png, http://ephy.in/wp-content/uploads/2014/11/clip_image0061.png, http://www.nilvalls.com/supernumerary-rainbow/, http://www.atoptics.co.uk/rainbows/ord34.htm

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.

Sources: http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/relmom.html, http://kaffee.50webs.com/Science/images/KTG.origin.of.pressure.gif, http://blazelabs.com/pics/reflabstrans.gif, http://global.jaxa.jp/activity/pr/brochure/files/sat28.pdf

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.

Sources: http://alexbeutel.com/webgl/voronoi.html, http://www.iue.tuwien.ac.at/phd/klima/node21.html, http://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/non_Euclid_curved/Geodesic3.gif, http://beautifulnow.is/bnow/the-quest-for-beautiful-data