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Supplementary Materials

In the interests of economy and to make the book more “Reader Friendly,” the publisher had me delete certain sections of the manuscript. I include some of this material for the benefit of the reader who would like to explore the subject more deeply, or who is curious about the supporting data for some of the conclusions drawn in the book

-Craig B. Smith

From the Preface:

First, a word about units. Today the world standard is the International System of units, referred to as SI, and based on the meter as the unit of length. For the convenience of the reader I show both SI and American/British units. These approximate equivalents will help in visualizing distances and dimensions. One meter, roughly one yard or 3 feet. A nautical mile, roughly 2 kilometers, slightly greater (15 percent more) than a statute mile. A knot (one nautical mile per hour), roughly 2 kilometers per hour. Most important, a nautical mile is equivalent to one minute (60 minutes to the degree) of latitude. Finally, conversion factors are found in the Appendix 2.

From Chapter 1

A Brief History of Ocean Exploration

Despite the dangers, humans continued to explore the oceans for a thousand years beyond the time of Homer, staying close to shore at first, then gradually venturing farther and farther offshore, seduced by the traditionally calm waters and idyllic weather of the Mediterranean. In 1,000 B.C the Phoenicians took control of the Mediterranean and made it a Phoenician lake. In their galleys, some 20 meters (57 feet) long, they explored the shores of the Mediterranean Sea, established cities, and eventually made their way to the Atlantic Ocean. If we believe Herodotus, a Phoenician crew was the first to circumnavigate Africa, taking three years to pass from the Red Sea, down the east coast, around the Cape of Good Hope, and back through the Straits of Gibraltar.[1] The Greeks learned much about sailing and navigation from the Phoenicians, who, having no compasses, navigated by the North Star. From 800 to 1000 A.D. another group of hardy oceanfaring adventurers emerged in northern Europe. From Scandinavia, Viking raiders reached England, France, and Spain, and traveled east to parts of Russia and coastal areas of the Baltic Sea. Piloting sturdy but light oceangoing vessels 20 to 24 meters (57 to 79 feet) long, they crossed the North Atlantic Ocean to Iceland and Greenland, and reached North America (Newfoundland) around 1000 A.D. At this same time, but half a world away, China was turning out  the world’s best sailors and navigators. The Chinese developed paper, produced accurate nautical charts, used astronomy for navigation, and began to explore the South China Sea. Chinese junks—some as long as 45 meters (148 feet) — were the most reliable oceangoing vessels built up to that time.[2]

When the Ming Dynasty emperor Zhu Di came to power, he rewarded several servants who had served him well. One, named Cheng Ho was put in charge of a shipbuilding program. At a shipyard in Nanking, Ho saw to the building of hundreds of vessels—some as long as 150 meters (492 feet)—to create a Treasure Fleet that was to explore all of the known oceans and develop trade with foreign nations. Cheng Ho led seven expeditions between 1405 and 1433, traveling south to cross the Bay of Bengal, the Arabian Sea, and the Indian Ocean and to the north, the East China Sea and the Sea of Japan. In the west, he reached the east coast of Africa, near the site of Mombassa, and in the northwest, traversed the Red Sea as far as Mecca and into the Persian Gulf. He also visited Sumatra, Indonesia, Thailand, and Borneo.

In 1424, the emperor (who had changed his name to Yong Le) died. The emperor’s son, Zhu Gaozhi, discontinued the voyages of the Treasure Fleet. But when he died, his son Zhu Zhanji (Zhu Di’s grandson) came to power and gave the order to resume the trips. Cheng Ho died on the way home following the seventh voyage, and the emperor closed the shipyard and idled the fleet.[3]

The Chinese withdrew into isolation. Even the construction of oceangoing vessels was eventually banned, and their great seafaring abilities and traditions faded into oblivion. Arab traders took the place of the Chinese, and by 1400 A.D. were in control of the trade routes and principal ports in the Indian Ocean. Their range extended from the Red Sea and Persian Gulf south to eastern Africa and the Spice Islands, but they feared venturing into the unknown of the South Atlantic.

Meanwhile, the Portuguese were exploring southward, establishing bases along the west coast of Africa, and in 1488 Bartolomeu Diaz rounded the Cape of Good Hope. This set the stage for Vasco da Gama to round the Cape and finally reach India (1498), in an effort to reduce dependence on Arab traders for the spices and other valued products from the Orient. Portuguese success led to Spanish concerns that the Portuguese would dominate the lucrative trade with east Asia, and eventually prepared the way for Columbus to prevail in his quest for royal approval of a voyage west—the ‘backdoor’ route to the Spice Islands and the riches of the Orient.

Discoverers of New Worlds—Columbus and Magellan

Upon departing from Spain, Columbus first sailed southwest along the coast of Africa until he reached the Canary Islands, then turned west. He planned for a voyage of 28 days, thinking that would suffice for the voyage to the Orient (Japan) that he anticipated was a mere 2,400 nautical miles (4,444 kilometers) distant. He arrived at this conclusion through a series of errors—using some incorrect data to start with—and then reduced the numbers still further for what can only be described as “marketing” purposes: to sell the voyage to his royal sponsors. As it was, the distance Columbus estimated for Japan was almost exactly the distance to the Bahamas, where he made his first landfall on October 12, 1492.[5]

His passage across the Atlantic was remarkable. His log shows days of steady sailing at speeds of 6, 8, even 10 knots through calm seas.[6] No major storms were encountered. Columbus kept two logs: a private one, in which he tracked his actual position, and a second one, which he shared with the crew. In the latter, he deliberately reduced the distance they’d traveled from Spain, fearing that if the crew believed the distance to be too great they would become convinced there was no way for them to sail home and would panic and mutiny. Columbus knew that they could return by first sailing northeast to catch the westerlies—the winds that blew east across the Atlantic, and that is exactly what they did.

Columbus’s accomplishment excited the world and triggered an age of exploration. Others followed in his footsteps—Cabral, to the coast of South America and then on to the discovery of Brazil in 1500. Then, 19 years later, came Magellan’s epic voyage. Fernão Magalhães was Portuguese, and like Columbus, sought the support of Spain when Portugal refused to support his grand plan to go east by sailing west. Eventually he secured the support needed, and on September 20, 1519, sailed from Spain and into the Atlantic with an armada of five vessels, known thereafter as the Armada de Molucca. Six months later, battered by recurring storms that had nearly sunk the fleet, and realizing he could not find the magical strait to the Spice Islands before winter fell on the fleet in its full fury, he resolved to find a safe place to spend the winter. This turned out to be a protected harbor near the tip of Argentina, known today as Puerto San Julian.[7]

But Puerto San Julian provided only temporary relief to Magellan; within days he faced mutiny on three of his five ships. He successfully quelled the mutinies and regained control. Then, during a break in the weather he sent one ship—the Santiago—south to look for the strait; it lingered, got caught in a storm, and was lost. Eventually, he recovered the crew and put everyone to work repairing and refitting the remaining vessels as best they could. On August 24, the long southern winter finally ending, he again set sail for the south, but could continue for only two days before being forced to seek refuge from another series of storms. Finally, in October he set sail again, and on October 21, 1520, discovered the strait that bears his name today.

Finding this strait was one thing; navigating it was another. With no charts to guide him and facing tides running as high as 7 meters (23 feet), fast-paced currents, and shifting winds, navigation became an immense challenge for Magellan. Even worse, while Magellan continued his struggle to find the way through the straits, his largest vessel, the San Antonio, succumbed to a mutinous navigator, and fled the straits to make its way back to Spain. When Magellan exited the strait on November 28, 1520, he was down to three vessels and short on rations. He worked his way north along the Chilean coast, finally catching the southeast trade winds near the Juan Fernandez Islands. Next came days of calm sailing that inspired Magellan to christen the Pacific mare pacificum—in Latin, “peaceful sea”—as the three vessels moved forward under the constant impulse of the trade winds.

By fluke or good fortune, Magellan avoided the thousands of islands, reefs, and atolls that abound in the South Pacific. But he did not make landfall until reaching the Marianas Islands (Guam), 98 days after leaving the straits. Many of the crew had died, and all suffered from scurvy and hunger. It was now March 6, 1521.

A year and a half later—on September 6, 1522—a heavily damaged vessel was observed approaching southern Spain. It was the Victoria, the last of Magellan’s ships, his remaining crew finally making it home to tell the story of his epoch voyage. The other two ships had been lost in storms; Magellan himself had been killed and buried in the Philippines, the victim of an ill-advised fight with natives. The 18 surviving crewmen on the Victoria could claim the first circumnavigation of the world. And not only that, as proof of Magellan’s acumen, they unloaded a cargo of 381 sacks of cloves, sufficient to make the trip profitable despite the loss of three vessels.[8]

From Chapter 2

Summary of Major currents

Note: While reading the next nine paragraphs, it is helpful to look at a world globe or map in order to visualize the circulation paths of ocean waters as I describe them. Alternatively, Figure 4 (See book) may help. In the Pacific, the Kuroshio Current (an extension of the North Equatorial Current), curves northerly past Japan and continues clockwise between the Aleutians and the Hawaiian Islands. Kuroshio means “black stream” in Japanese. Similar to the Gulf Stream, it is around 100 kilometers (62 miles) wide and transports large amounts of warm tropical water north to colder zones. The Kuroshio Current can reach speeds of 3 to 4 knots. The confrontation of this stream with storms coming down from the north is one of the sources of giant waves. Continuing the clockwise circulation, this current becomes the Northern Pacific Current, which branches, a portion turning north along Canada and Alaska, eventually forming the Alaska and Aleutian Currents, other sources of giant waves. The southern portion becomes the California Current flowing southeastward and down the coast of California and Baja California at an average speed of 0.8 knots, eventually merging back into the North Equatorial Current flowing west. During the winter, a weak countercurrent, called the Davidson Current, flows northwestward from Baja California to British Columbia.

The South Equatorial Current behaves similarly, curving southward along Australia, where it is known as the East Australia Current, past New Zealand, and eventually back toward the tip of South America, where it divides, a portion flowing into the Atlantic Ocean and the balance flowing northward along the west coast of South America as the Humboldt Current.

In the Atlantic, that portion of the South Equatorial Current that flows north along South America merges with the North Equatorial Current and flows between the Windward Islands into the Caribbean Sea, heading westerly toward the Yucatan Peninsula and then into the Gulf of Mexico, where it creates a variable Loop Current that circulates in the Gulf of Mexico. Near the Straits of Florida, this current, the Antilles Current, and others merge to form the Gulf Stream. The confluence of several powerful currents in the Gulf of Mexico and their passage in the Gulf and around Cuba, then through the Straits of Florida and the Bahamas, is often responsible for changeable and dangerous weather conditions.

The Gulf Stream, first identified by Dampier and later described by Benjamin Franklin, is remarkable for the volume of warm water it carries northward and its distinctive deep blue color. It is 80 kilometers (50 miles) wide but can form eddies and snaking as it meanders. Its speed is 2 to 4 knots off of the coast of Florida, but can be as much as 4 to 5 knots. It moves northeasterly past the Grand Banks, eventually becoming the North Atlantic Current. In the eastern Atlantic this current divides, one portion branching northeast toward Iceland and Norway (the Irminger Current and Norway Current), another portion going north along the west coast of Greenland, and still another portion moving east and then south toward the Canary Islands as it is deflected by the coast of Europe. It eventually rejoins the North Equatorial Current.

This pattern of clockwise circulating currents in the Atlantic Ocean is remarkable in another respect. In the central region bordered by the currents is a large eddy, bounding an area with no significant currents. This is known as the Sargasso Sea because of the large quantities of sargassum (a kind of seaweed) encountered there.

In the South Atlantic, the current moves south along Brazil, encounters the Falklands Current, and then curves east toward the Cape of Good Hope, where a portion turns north along the west coast of Africa as the Benguela Current. The Benguela Current is further strengthened by part of the Agulhas Current coming from the Indian Ocean and around the tip of South Africa creating a strong current that flows at speeds of around 0.33 knots.

In the Indian Ocean, the situation is similar to that in the Pacific and Atlantic Oceans—two west-flowing equatorial currents dominate. In the northern Indian Ocean (the Arabian Sea and Bay of Bengal) some of the prevailing currents reverse direction from winter to summer; for example, the Somali Current reverses direction in the northern hemisphere summer and flows north at 5 knots or more. In the southern Indian Ocean, the South Equatorial Current flows toward Africa, divides as it flows south around Madagascar, then rejoins to form the powerful Agulhas Current that flows south around the Cape of Good Hope at speeds of  3 to 4 knots. Of this, we shall learn much more later.

The Southern Oceans of Antarctica are the most desolate and foreboding of all. The Antarctic Circumpolar Current flows west around the entire world, no continents obstructing its movement, driven by the strong prevailing winds. It is fed by waters from each of the oceans—the Brazil Current, the Agulhas Current, and others—and transports waters between them.

In the Artic Ocean, on the Pacific side, there is a weak current north through the Bering Strait and a southerly flow along Siberia that becomes the Kamchatka Current. From the Atlantic, a current flows northeasterly along the coast of Norway into the Arctic Ocean, then turns north, crosses the North Pole, and emerges along the east coast of Greenland as the East Greenland Current flowing back into the North Atlantic.

Here I beg the reader’s indulgence for this seemingly lengthy description of currents, which I have tried to make as concise as possible. (For the seasoned sailor or navigator, please ignore the omissions; they do not contribute materially to the purposes of this book.)

From Chapter 2:

The Beaufort Wind Scale

The Beaufort Wind Scale

 Wind force Wind Description Wind speed m/sec       knots Wind effect on the sea Probable wave height meters Average  Max 0 Calm 0-0.2           <1 Sea like a mirror --            -- 1 Light air 0.3-1.5         1-3 Scaly ripples without foam crests 0.1           0.1 2 Light breeze 1.6-3.3         4-6 Small wavelets, glassy, non- breaking crests 0.2           0.3 3 Gentle breeze 3.4-5.4        7-10 Large wavelets, crests begin to break, scattered white horses (plumes of spray) 0.6            1.0 4 Moderate breeze 5.5-7.9        11-16 Small waves with frequent white Horses 1.0            1.5 5 Fresh breeze 8-10.7         17-21 Moderate waves, many white Horses 2.0             2.5 6 Strong breeze 10.8-13.8    22-27 Large waves, white foam crests, some spray 3.0             4.0 7 Near gale 13.9-17.1    28-33 Mounting sea with foam blown in streaks down wind 4.0             5.5 8 Gale 17.2-20.7    34-40 Moderately high waves, crests begin to break into spindrift 5.5             7.5 9 Strong gale 20.8-24.4    41-47 High waves, dense foam along direction of wind; crests begin to topple over, spray can affect visibility 7.0             10 10 Storm 24.5-28.4    48-55 Very high waves with long over- hanging crests. Heavy sea roll, sea surface white, limited visibility 9.0             12.5 11 Violent storm 28.5-32.6    56-63 Exceptionally high waves. Other ships lost to view.  Sea completely covered with foam patches downwind. Poor visibility 11.5           16.0 12 Hurricane >32.7          >64 Huge waves. Air filled with foam and spray. Sea completely white with driving spray, visibility bad 14.0                            19   and greater

Source: Based on Observer’s Handbook, UK Meteorology Office

Today, the Beaufort Scale has been supplemented by the Universal Sea State Code. Under this system, SS0 (sea state zero) is described as “Sea like a mirror, wind less than one knot, wave height zero; SS4 is “Rough sea; moderate waves, many crests break, whitecaps, some wind-blown spray;  winds moderate to strong breeze, 11-27 knots; wind whistles in rigging, average significant wave heights 1.2 to 2.4 meters (4 to 8 feet).” SS8 is “Mountainous seas; very high-rolling breaking waves; sea surface foam-covered; very poor visibility; winds at storm level, 55-63 knots; waves 9.1 to 13.7 meters (30 to 45 feet.)”

Excerpt from Chap 3

Probability of Large Waves

If we consider waves as an example of a stochastic process—a process that follows some form of a probability distribution—wave behavior can be analyzed statistically but cannot be predicted precisely. In other words, weather forecasters are unable to say: “A 20-meter wave will occur at such and such a location at such and such a time,” but they can say something like this: “There is likelihood that 8 percent of the waves that occur in a year at this location will be 20 meters or higher.”

Now the question becomes, What kind of probability distribution? Research has found that in deep water, the height of small ocean waves obeys a Gaussian process, named after Karl Friedrich Gauss (1777-1855), a German mathematician. In the Gaussian process, the height of the waves follows a normal distribution.

While the term may seem intimidating, we’re all familiar with a normal distribution, sometimes called a “bell curve” due to its shape. A case in point: a teacher believing a class to be large enough that the students’ abilities (or perhaps study habits) were a Gaussian process, might grade “on the curve.” Another case in point: An engineer cuts 1,000 samples from the same batch of steel reinforcing rod, places them in a testing machine, and pulls on them until they snap. The test results show that most break at a tensile force of 80,000 pounds per square inch. However, some break as low as 70,000, others withstand 90,000. If the test results are graphed, a bell-shaped curve results. A normal distribution has a mean value; in the example cited above, this would be 80,000.

I stated earlier that weather forecasters report wave heights as Hs, defined as the average of the highest one-third measured (or predicted, in the case of forecasts) wave heights. To estimate this value, a further assumption is needed—that is, that the Gaussian process is narrow banded. This means that the wave energy is grouped within a narrow band of periods. Waves produced by moderate winds in deep water have this property. For this case, wave amplitudes follow a Rayleigh probability law.[9]

Figure 8 (See book) shows a theoretical Rayleigh Distribution. The vertical axis measures the probability that a particular wave height will occur, while the horizontal axis is the wave height. The figure shows the lowest 10 percent of the waves, the most probable wave height Hp, the average wave height HA, the significant wave height Hs, and the highest 10 percent of the wave heights.

Figure 8: Rayleigh Distribution of Wave Heights[10]

The significant wave height Hs is marked on the graph and is equal to 1.6 HAve.[11] The probability that a wave greater than Hs will occur is shown by the shaded area under the curve to the right of Hs. If the mathematics is carried out, this area is found to be 13.5 percent of the total, meaning that there is a 13.5 percent chance that a wave greater than Hs will occur, or that roughly one in seven waves will be larger than Hs. This result is corroborated in a number of cases (but not all) by buoy readings and measurements on offshore oil platforms, where hundreds of measurements of Hs and the maximum wave for a series can be compared. Compare this to surfer’s lore, as described in Chapter 6. Young notes that this compares favorably with the oft-stated mariner’s view that every seventh wave in a set is larger.[12]

A mathematician would recognize that the Rayleigh distribution goes on forever. In other words, there is a vanishingly small probability of very, very large waves. If we knew how many wave records were represented in the Rayleigh distribution, we could estimate Hmax . When the number of waves is not known, an approximate relationship is Hmax = 1.77 Hs as stated by Muga.[13] If the wave height is much greater than this value, it falls outside of the range we might reasonably expect. This is what has given rise to the term “rogue” or “freak” wave. In a random sea, how many waves would it take before you experienced Hmax? In 20 waves, there is about a 5 percent chance of reaching Hmax, and in 200 waves, a 5 percent chance of reaching 2.0Hs. An extreme wave—one greater than 2.2 to 2.4 times Hs—has a 5 percent chance of occurring in 1,000 to 4,000 waves, assuming a constant sea.[14] There would be 5 waves per minute, 300 waves per hour, if the waves had a 12 second period. Thus in traveling 3.3 to 13.3 hours in such a sea, a vessel would have a 5 percent chance of experiencing an extreme wave. During this time, at 10 knots, the vessel would have moved 33 to 133 nautical miles, hopefully to an area where Hs was smaller and the consequences of encountering an extreme wave, less severe.

For larger waves, for variable wind conditions, such as those associated with hurricanes, or for waves in shallow water, more complex methods are required. As waves approach the coast, they undergo a transition from a Gaussian to a non-Gaussian process, and must be handled differently.[15] Waves in shallow waters and very large waves are nonlinear and must be analyzed by other means. Extreme waves have crests that are several times higher than the distance from the center line to the bottom of the trough, and they are steeper than other waves.

Figure 9 (See book) is an actual U.S. Department of Commerce, National Oceanic and Atmospheric Administration marine weather forecast for the North Pacific on March 7, 2005. Note the storm centered at latitude 30 degrees north, longitude 150 degrees west, northeast of the Hawaiian Islands. The forecast shows 40-knot winds and waves with12.8 meter (42 foot) significant heights at the center of the storm. These waves had a period of 12 seconds. Looks like a spot to avoid, if you had the option. (See Chapter 5 for more about this particular storm.)

Figure 9: Typical NOAA marine weather wind/wave forecast

A new tool for measuring wave heights is the satellite. As a satellite orbits the earth and passes over the oceans, it collects a huge amount of data. Due to the sheer effort involved in analyzing the data within a reasonable time, the data are averaged over a period of days and a spatial grid of 2 degrees by 2 degrees (120 nautical miles by 120 nautical miles or 222 by 222 kilometers).[16] The practical implication of this is that individual, infrequent wave events are not detected. Thus these data provide reliable estimates of the significant wave height Hs on a global basis, but not the extreme wave height, Hext. In Chapter 8 I describe more recent research into satellite observations that have been designed to detect the extreme wave height Hext, and the astonishing results that have been obtained.

The satellites reveal two major bands circling the world’s oceans where the greatest values of significant wave height occur. These are areas where the significant wave height is routinely almost 20 feet (6 meters.) As you might expect, there is a distinct trend—there are more big waves in the winter. Figure 11 shows the situation in February—winter in the northern hemisphere. The darkest area corresponds to a significant wave height of 6 meters, the lighter shades, 4 and 5 meter heights.  Note that they encompasses a broad area of the North Atlantic, England to Newfoundland and in the North Pacific, from the Gulf of Alaska  to Japan, centered around latitude 50 degrees north. Meanwhile, at this time—summer in the southern hemisphere—the shaded area is centered along latitude 50 degrees south.

Figure 10: Global significant wave heights Hs, February

Next look at Figure 11, the same data for August—winter in the southern hemisphere. The shaded band has broadened into a swath of rough seas extending clear around the world, while in the northern hemisphere the shaded areas are gone. In other words, conditions in the Southern Ocean remain severe most of the year. Also note the absence of large waves in the tropical zones near the equator. This area is subject to a different condition, that of tropical cyclones. These satellite observations are not programmed to detect such transient events as hurricanes. (In Chapter 4 we will examine wave heights generated by storms and hurricanes.)

Figure 11: Global significant wave heights Hs, August

If the world’s major oceans are sliced along a longitudinal meridian in their center, the variation of significant wave height with latitude can be examined. If this is done, Hs increases from around 4 meters at 60 degrees north, to 6 meters at 50 degrees north, and then declines to 2 to 3 meters (6 to 10 feet) at the equator, again increasing to around 6.2 meters (20 feet) at 50 degrees south latitude.

No wonder sailors call 50 degrees south “the furious fifties.”

From Chapter 4

The Occurrence of hurricanes

• North Atlantic and Caribbean: from Venezuela on the south to the East Coast of the United States and Central America on the west, Newfoundland on the north, and eastward to Africa. Season: June 1 to November 30; peak: August to October.
• Northeastern Pacific: from Hawaii on the west to Mexico and Central America on the east, between latitude 10 degrees and 30 degrees north. Season: May 15 to November 30: peak; late August, early September.
• Northwestern Pacific: Southeast Asia on the west, Japan and Siberia on the north, 160 degrees west longitude as the eastern boundary, and latitude 10 degrees north as the southern boundary. Season: July to November; peak: late August, early September.
• North Indian Ocean: Bay of Bengal. Season: April to December; double peak: May and November. Severe tropical cyclones occur from April to June and late September to early December.
• Southwestern Indian Ocean and Australia-southeastern Indian Ocean: from the east coast of southern Africa on the west to mid-Indian Ocean on the east, between 10 degrees and 35 degrees south latitude. Season: late October to May, with a double peak, mid-January and mid-February to March.
• Southwest Pacific and Australia: from Australia’s east coast and the Coral Sea , east to longitude 180 degrees west, south to 35 degrees south latitude; also on Australia’s west coast. Season: October to May, peak in late February, early March. [17]

From Chapter 4

The Saffir-Simpson Hurricane Scale[18]

The strength of hurricanes is rated 1 to 5 on the Saffir-Simpson Hurricane Scale based on the hurricane's intensity at the time of reporting. The scale is used to give an estimate of the potential property damage and flooding expected along the coast from a hurricane landfall. Wind speed is the determining factor in the scale, as storm surge values are highly dependent on the slope of the continental shelf in the landfall region.

Category One Hurricane:

Winds 64-82 knots (74-95 miles per hour). Storm surge generally 1.2 to 1.5 meters above normal. Central pressure less than 980 millibars.  No real damage to building structures. Damage primarily to unanchored mobile homes, shrubbery, and trees. Some damage to poorly constructed signs. Also, some coastal road flooding and minor pier damage. Hurricanes Danny of 1997 and Gaston of 2004 were category one hurricanes at peak intensity.

Category Two Hurricane:

Winds 83-95 knots (96-110 miles per hour). Storm surge generally 1.8 to 2.4 meters above normal. Central pressure 975-965 millibars. Some roofing material, door, and window damage of buildings. Considerable damage to shrubbery and trees, some trees blown down. Considerable damage to mobile homes, poorly constructed signs, and piers. Coastal and low-lying escape routes flood 2-4 hours before arrival of the hurricane center. Small craft in unprotected anchorages break moorings. Hurricane Bonnie of 1998 was a Category Two hurricane when it hit the North Carolina coast, while Hurricane Frances was a category two hurricane when it hit Florida.

Category Three Hurricane:

Winds 96-113 knots (111-130 miles per hour). Storm surge generally 2.7 to 3.7 meters above normal. Central pressure 964-945 millibars. Some structural damage to small residences and utility buildings and a minor amount of curtain wall failures. Damage to shrubbery and trees, foliage blown off trees and large trees blown down. Mobile homes and poorly constructed signs are destroyed. Low-lying escape routes are cut by rising water 3-5 hours before arrival of the center of the hurricane. Flooding near the coast destroys smaller structures, larger structures damaged by battering from floating debris. Terrain lower than 1.5 meters (5 feet) above mean sea level may be flooded inland 13 kilometers (8 miles) or more. Evacuation of low-lying residences within several blocks of the shoreline may be required. Hurricanes Roxanne of 1995 and hurricanes Ivan and Jeanne (2004) were category three hurricanes at landfall on the Yucatan Peninsula of Mexico and in Alabama and Florida, respectively.

Category Four Hurricane:

Winds 114-135 knots (131-155 mph). Storm surge generally 4 to 5.5 meters (13-18 feet) above normal. Central pressure 944-920 millibars. More extensive curtain wall failures with some complete roof structure failures on small residences. Shrubs, trees, and all signs are blown down. Complete destruction of mobile homes. Extensive damage to doors and windows. Low-lying escape routes may be cut by rising water 3-5 hours before arrival of the center of the hurricane. Major damage to lower floors of structures near the shore. Terrain lower than 3 meters (10 feet) above sea level may be flooded requiring massive evacuation of residential areas as far inland as 10 kilometers (6 miles). Hurricane Luis of 1995 was a category four hurricane while moving over the Leeward Islands. Hurricane Charley of 2004 also reached category four status when it hit Florida, and most recently hurricane Katrina in 2005.

Category Five Hurricane:

Winds greater than 135 knots (155 miles per hour). Storm surge generally greater than 5.5 meters (18 feet) above normal. Central pressure less than 920 millibars. Complete roof failure on many residences and industrial buildings. Some complete building failures with small utility buildings blown over or away. All shrubs, trees, and signs blown down. Complete destruction of mobile homes. Severe and extensive window and door damage. Low-lying escape routes are cut by rising water 3-5 hours before arrival of the center of the hurricane. Major damage to lower floors of all structures located less than 4.6 meters (15 feet) above sea level and within 460 meters (1,500 feet) of the shoreline. Massive evacuation of residential areas on low ground within 8 to 16 kilometers (5-10 miles) of the shoreline may be required. Hurricane Mitch of 1998 was a category five hurricane at peak intensity over the western Caribbean. Hurricane Andrew of 1992 was a category five hurricane at peak intensity and is one of the strongest tropical cyclones to hit Florida.

From Chapter 4

Hurricane-generated wave heights

Stochastic methods similar to those described in Chapter 3 can be used to forecast wave heights caused by hurricanes.[19] Ochi suggests that hurricane-generated waves can be modeled as a Gaussian random process, and therefore extreme wave heights can be calculated from a known or estimated wave spectrum.[20] The approach is to develop a wave spectrum that gives the time averaged wave energy versus frequency. The spectra can then be correlated with the expected wave height. The hurricane spectrum differs from an ordinary wind spectrum because it has a sharp peak rather than being broad. If the spectrum is measured by an ocean buoy in the path of the storm, it will grow as the hurricane gets closer. (Figure 15).

Figure 15: Hurricane energy spectrum[21]

Note that from the initial point of measurement, in 10 hours the significant wave height has doubled from 6.6 meters to 13.5 meters!

From Chapter 4

Wind speed change from hurricane

Figure 16 shows the wind speed recorded at Barrow Island, off the northwest coast of Australia, just below latitude 20 degrees south. The solid line is the mathematical prediction; the dots are the recorded values for hurricane Ian in 1992. Note how the winds begin to rise late on March 1, reach a maximum at 35 meters per second (66 knots) early on March 2, then drop to 5 meters per second (9.5 knots) as the eye of the hurricane passes, and then increase again as the other side of the storm passes over the island late on March 2.

Figure 16: Wind Speed as Eye of Hurricane Passes[22]

From Chapter 4

Measured wave heights during hurricanes

Figure 17 shows some of the data collected from seven hurricanes in various stages of growth. Remember, the maximum wave heights can be higher by as much as 30 percent or more than the significant wave height!

Figure 17: Wave Height vs. Hurricane Wind Speed[23]

The figure shows that the significant wave height in meters is about one fourth (actually 24 percent) of the hurricane sustained wind speed expressed in meters per second at the standard elevation of 10 meters above sea level.

From Chapter 4

Forecast Accuracy

National weather services use several models for predicting the track and intensity of hurricanes. Track forecasts are the latitude and longitude of the storm center, while intensity refers to the maximum sustained surface wind. Forecasts are typically issued for 12, 24, 36, 48, and 72 hours. Two main types of mathematical models are used: one type predicts the storm track; the second type is used to predict intensity. Some examples of models are BAM, a computer model that tracks the early trajectory of storms; UKMET, a global model developed by the United Kingdom Meteorological Office; and NOGAPS, a global atmospheric model developed by the United States Navy. For estimating intensity, the National Hurricane Center uses programs such as the Statistical Hurricane Intensity Forecast (SHIFOR), the Geophysical Fluid Dynamics laboratory (GFDL) model, or SHIPS. Ironically, the last acronym stands for “Statistical Hurricane Intensity Prediction Scheme.”

Details of these models are outside the purpose of this book; however, readers interested in additional information are advised to consult the National Hurricane Center Web site for an overview of the most recent models used for forecasting. The Web site also provides references and links to more detailed technical literature.[24]

From Chapter 5

Sources for Wave information

There are a number of sources for wave and weather information. Global weather forecasts for up to ten days are provided by the European Center for Medium-Range Weather Forecasts at http://www.ecmwf.int/. A general source for marine weather information in the Atlantic and Pacific Oceans is http://www.nws.noaa.gov.  Another excellent source is a United States Navy Web site, https://www.fnmoc.navy.mil/PUBLIC/WAM, commonly referred to as the “WAM” site, features colored maps of the North and South Atlantic oceans, the North and South Pacific oceans, and the Indian Ocean, showing wave directions and significant wave heights. The color codes range from dark blue for 0-1 meter, (0-3 feet) wave heights, up to dark brown 14.6 meters (48 feet) wave heights. There is no scale to indicate 30.5 meter (100 feet) waves. The forecasts for each region extend out 6 days in 12-hour intervals, so the movements of large waves can be anticipated. Plate 7 (See book) shows a WAM forecast for April 16, 2005, at 0 hours “Zulu” (Greenwich) time. The biggest waves (about 11 meter or 36 feet) can be seen at latitude 60 degrees south, off the coast of Antarctica. They can be seen propagating north past Madagascar, in the opposite direction of the Agulhas current, but no big waves are indicated in this region in the forecast.

Plate 7: U.S. Navy Indian Ocean Wave Forecast

The United States National Oceanic and Atmospheric Administration, as well as Canada, Scripps Institute, and other entities operate a series of buoys in the northwest Pacific and California coastal areas. These also can be accessed using the Internet. For example, www.ndbc.noaa.gov will take you to the locations of moored buoys scattered around the Pacific, as well as to the locations of drifting buoys. To obtain the real time data from a buoy, click on its image on the map. I did this for station 46006, which bears the name of “SE PAPA.” It is a fixed buoy located 600 nautical miles west of Eureka, California, at 40.8 north latitude and 137.5 degrees west longitude. Reviewing the record for the last two days, I could see a clear pattern of the wind speed building to 29 knots on March 7, with gusts to 35 knots, a significant wave height of 5 meters, and a period of 14.3 seconds.

To see an example of a local conditions report go to http://facs.scripps.edu/surf/images, which will lead you to a series of coastal buoys in the Southern California bight. On March 10, 2005, the buoy at Goleta Point was showing the predominant swell arriving from the west (around 260 degrees), with a dominant period of 18 seconds and a significant wave height of 2.7 meters. Here again, the height was steadily building.

In California, as in Hawaii, Australia, Brazil, Tahiti, and other international surfing spots, there are commercial services that provide surf forecasts. An example is www.stormsurf.com. On March 8, 2005, this site predicted rising surf on March 9 and 10. Farther south, near La Jolla, California, the forecast indicated that select breaks with 100 percent exposure to the swell could reach up to 1.8-2.1 meters at 17 to 20 second periods, and possibly 3-4.3 meters wave faces. For March 10, the forecast concluded with a final note: Proceed with caution.

From Chap 7

What is the significant wave height when multiple swells are present?

Trying to determine how high the waves are in chaotic seas might seem to be nearly impossible, but weather forecasters have devised methods, based on the randomness of chaotic seas, that they use.[25]Assuming that the significant heights of both the swell and the wind-driven sea are known, the combined height can be approximated as the square root of the sum of the squares, or:

Hcomb = [(Hswell)2 + (Hsea)2]0.5

where Hcomb is the significant height of the combined seas.

As an example, if wind waves with Hs = 1 meter (3.3 feet) combine with a 2 meter (6.6 foot) high swell, the combined significant height would be:

Hcomb = [(2)2 + (1)2]0.5 = [4+1]0.5 = 2.24 meters (7.33 feet)

The logic behind this approach derives from the fact that the energy of waves is proportional to the square of their height. This estimate is subject to the usual cautions mentioned previously—that is, the wave heights are randomly distributed.

From Chapter 8:

Any observer who spends time in the ocean soon learns that wave patterns are more frequently complex than simple. This fact was used to advantage by the early Polynesian navigators, who discovered that there were repetitive patterns in the confused seas they experienced as they ventured from island to island. The ancient Polynesians knew that swell in the Pacific followed predictable paths, depending on the time of year. When one of the prevailing swells struck an island, certain wave patterns were established in a manner analogous to the boulder in the center of a rapidly moving stream described above.

As early as the time of the first voyage of Captain James Cook, the navigational capabilities of Polynesian sailors became apparent. In his July 13, 1769 entry in his sea journal, Cook relates that he was able to convince a priest and navigator named Tupia to accompany him on the continuation of his voyage when he sailed away from Matavai Bay, Tahiti.[26] From his experiences with Tupia, Cook concluded that the Polynesians were fully capable of sailing from one island to another, for a distance of several hundred leagues (more than one thousand kilometers.) Over a period of time, Polynesians populated a vast area of the Pacific Ocean, over 80 degrees of longitude (from 140 degrees east to 140 degrees west), or 4,800 nautical miles long, and over 60 degrees of latitude (30 degrees south to 30 degrees north, or 3,600 nautical miles wide. In most cases, they did it on island-hopping journeys of 50 to 200 nautical miles.

How did they do it? How did they manage to avoid deadly reefs and make accurate landfalls on remote islands without benefit of compass, chart, or sextant?

In the 1900s it became apparent that some navigators who knew the ancient techniques were still living, but they were the last of a small group that was slowly dying off. In 1965, while circumnavigating the world in a 40 foot catamaran, sailor David Lewis learned the rudiments of their techniques, and then successfully sailed from Tahiti to New Zealand, a distance of around 2,200 nautical miles, without using navigation instruments. Convinced of the validity of the methods, he returned in 1968-69 to study and document the ancient navigation techniques, sailing in a 39 foot ketch to a number of South Pacific islands. On these voyages he depended entirely on the skills of several navigators whom he invited to guide him.[27]

About 15 years later after conducting some preliminary research, a young sailor, Steve Thomas, took passage to Satawal Island in the Caroline Island group, where he succeeded in apprenticing himself to a navigator named Mau Piailug. Steve lived as a member of Piailug’s family, and from him learned the navigational techniques that had been handed down orally from generation to generation.[28]

Modern navigation uses the compass to establish heading (direction of travel), charts to locate the position of the vessel relative to its destination, and such instruments as chronometers, sextants, loran, or global positioning satellites to “fix” (determine) the position of the vessel.

In the Polynesian system, an initial heading was established by back sighting landmarks on the departure island; from this, an estimate of the set of the current could be made and the course adjusted appropriately. Steering at night was done by observing the rising or setting of known stars. During daylight or when stars were obscured by clouds, swell patterns were used for navigation.

By lengthy training and memorization, the navigator learned the positions of 30 or more prominent stars. During the night the vessel was steered in the direction of a star known to rise over the destination island. Once this star had risen too high above the horizon to be useful for steering, the navigator steered to a second star that rose in the same direction, or to an alternate star that was “off-course” a known amount, for which the heading of the vessel was adjusted.

This method is unique in another respect. In the Polynesian navigator’s mental image, his vessel was fixed and the destination island “moved” into position under various stars, until the island reached a position under the star that told him he had arrived. Contrast this to today’s navigation method whereby our vessel is moving and the destination island is a fixed point that we seek to reach by determining its distance and heading.

Polynesian navigators must retain a mental image of the positions of 32 rising or setting stars, arranged in a manner analogous to the points of a compass. Thus Polaris marks north, rising Little Dipper (Ursae Minoris) marks roughly 15 degrees, rising Big Dipper (Ursae Majoris), 27 degrees, rising Vega, 40 degrees. Similarly, setting Little Dipper marks roughly 345 degrees, setting Big Dipper 333 degrees, setting Vega, 320 degrees. Other stars fill out the remaining points on the star map; the formal name for such a device is a sidereal compass.

Thomas describes a model of a sidereal compass that Mau Piailug constructed on the beach with a central rock and 32 pieces of coral placed around it in a circle, each piece of coral representing a particular star.[29]

During daylight, when no stars were visible, the navigator made use of the ocean swell to judge the heading of the vessel. Navigators were trained to recognize eight dominant swells. During the winter months, dominant swells came from the northeast or east under the influence of the trade winds. With a northerly heading and an east swell, the navigator knew the heading was correct if the vessel rocked. On an easterly course into an east swell, the vessel would pitch, bow rising and then falling as the vessel rode over the swells. To maintain a northwesterly heading, the navigator would adjust the sail and steering oar positions until the vessel responded with a combined pitching and rolling motion in the right proportions. The best way to do this, I’ve been told, is to lie flat on your back on the deck and look up at a cloud or star. The motion of the boat is easier to sense this way than staring at the horizon.

Clearly this process required considerable practice and skill, because, as we have seen, there are numerous waves in a confused sea. Wind waves may ride on top of swell; there might be cross swell from distant storms, and so on. The navigator had to discriminate to find the dominant swell within this melee of ocean waves.

Polynesian navigators became familiar with these patterns and in combination with the positions of the stars they could observe overhead, used them to navigate from island to island over long distances. The unique patterns established by the prevailing winds and currents in the vicinity of each island enabled the navigators to recognize where they were. To pass on the knowledge from generation to generation, they constructed “charts” made of sticks laced together to illustrate the wave patterns, using shells to mark the positions of islands.[30] Examples can be seen in the Bishop Museum, Honolulu and in the Nautical Museum, Newport Beach, California. The most skilled navigators could sense when they approached their destination by subtle shifts in the motion of their vessels as the wave pattern changed.

Within 20 to 30 nautical miles of the destination island, navigators relied on a number of different indicators. First, waves reflected back from the island (if approaching from the direction of the dominant swell) will cause the vessel to start a gentle pitching motion. If not coming with the swell, the vessel will encounter other wave patterns created by the refraction of the dominant swell as it passes the island. Navigators were able to recognize a number of different wave patterns; each had been given a specific name.

Other signs provide important indicators of position. Certain seagoing birds, known to frequent specific islands, would start appearing at distances of 20 to 30 nautical miles. Floating vegetation and even certain species of fish could also provide positive identification.

Once, while on a fishing trip out from Midway Island, we’d left in the morning at dawn. Later in the day I happened to look back in the direction of the island. The low-lying island was now over the horizon and invisible, but its location was clearly evident by a turquoise-green color in the clouds above it. This was caused by sunlight reflecting the island and lagoon onto the clouds and could be seen at a great distance. Clouds are formed by moisture-laden warm air rising over islands. At other times, a bright column or glow can be seen on the horizon, due to the reflection of sun or moon from shallow water or a lagoon; this is known as the loom of land.

As the Polynesians had no means of determining longitude, on longer voyages they usually sailed north or south to the approximate latitude of their destination. They watched zenith stars, or stars known to pass directly over the island to which they were steering. Once they came abreast of that position, they would tack and run downwind to their destination.

This is how the ancient Polynesians first sailed from the Marquesas Islands to the big island of Hawaii. First they sailed north to the Equator under the influence of the southeast trade winds, struggled through the doldrums (and were probably driven west by the Equatorial Counter Current), and then caught the northeast trades and ran downwind to Hawaii, following the orange beacon of its zenith star, Arcturus.

As for Thomas, he memorized the sailing directions for various islands in the Carolines and accompanied the Satawal navigators on several voyages to outlying islands. He carefully documented their methods, noting the stars they used and how the wind and swell patterns changed with the seasons. To accomplish this, he had to become proficient in their language as well.  There is, however, a certain sadness to his book. In reading it, one senses the twilight of the ancient skills that granted self-sufficiency to the islanders. Their sails and canoes replaced by outboard motors, they must now hold jobs to pay for fuel and supplies, and the old ways—those that had enabled them to populate a vast region of Oceana—appear doomed.

In the 1970s, a group of Hawaiian researchers constructed the Hokule‘a, a 60 foot-long replica of an ancient Polynesian double voyaging canoe.[31] The Hokule‘a was successfully sailed from Hawaii to Tahiti and back.

Hokule’a departed from Honolua, Maui, on May 1, 1976, and reached Papeete, Tahiti, 33 days later. The navigator on that trip was Mau Piailug, whom Stephen Thomas was later to meet and study under. Also on the crew were Ben Finney and Tommy Holmes, two of the cofounders of the Polynesian Voyaging Society; David Lewis, who has studied Polynesian navigation methods in the late 1960s; and 11 other crew members. Under Piailug’s guidance, the 3,000 nautical mile trip was accomplished without instruments. The voyage was significant because it established beyond question that the Polynesians, using the ancient methods of navigation, were able to explore and eventually settle vast expanses of the Pacific Ocean.[32]

On the return trip a few weeks later, Piailug remained behind and a different crew brought the boat back to Hawaii. In July, this time navigating with instruments, it took 22 days to make the trip north. The new crew included a young Hawaiian named Nainoa Thompson, who subsequently studied navigation under Piailug and later became the first Hawaiian navigator to guide Hokule’a on long voyages without instruments.

With these two successful trips, there was strong interest in further explorations, and in 1978, Hokule’a set sail again. However, the vessel encountered rough weather almost immediately, and before leaving Hawaiian waters, a tragedy occurred. Through my brother, Ken Smith, a well-known water polo coach and educator in Hawaii, I was introduced to Marion Lyman-Mersereau, who told me about her experiences on Hokule’a.

Chapter 9: The Pull of the Moon

(This chapter was deleted from the original manuscript)

Imagine a wave that stretches halfway around the world, has a period of 12 hours and 25 minutes, and is moving at hundreds of miles per hour in the open sea.[33] As surprising as it might seem, if you have spent any time on or near the ocean, you’ve experienced such a wave. The crests of this wave are known as high tides; its troughs, as low tides.

The rise and fall of tides along ocean shores has been recognized since ancient times. When the first sailors struck out tentatively in primitive vessels to cross bodies of water, they knew that there were opportune moments to depart from and to return to safe havens along the coast or in the mouths of rivers. The flow of water caused by the tides could be a help or a hindrance to primitive craft that depended on oars or sails for mobility. “To sail with the morning tide” is more than an expression; it accurately states a pragmatic requirement for moving a vessel out of many a harbor, particularly in the days before boats were powered by engines.

Sometimes the obvious has to be relearned. In Marina Del Rey, California, the rise and fall of the tides is noticeable but the associated current is weak. When a sailor returns or departs from a slip there, his concern is primarily with gauging the effect of whatever wind might be blowing at the time. After several years of docking Dreams at Deauville Marina in Marina Del Rey, I moved to Newport Beach and had to find a new slip. The slip I eventually obtained was in a marina along the main channel of the harbor. Newport Harbor is a long bay, running roughly northwest-southeast, with the harbor mouth at the southeast end (See Figure 23.) To the north of the main harbor is another small boat harbor and beyond that an extensive but shallow lagoon and wetlands known as the Back Bay. As the tide rises, water fills the main harbor then flows into the Back Bay (a flood tide), and when the tide falls, the process reverses and water flows out (an ebb tide). The net effect of this is that a strong current of several knots can flow in the main channel. The tidal range (maximum rise and fall of the water level) is 1.2 to 2.4 meters (4 to 8 feet).

As I approached my new slip for the first time on a Saturday, the slips on either side of mine held boats full of people engaged in an afternoon party. Entering the slip involved an approach from the southeast, followed by a sharp turn to starboard. Meanwhile it was an ebb tide and a strong current flowed down the main channel in a direction opposite to mine. As I made the turn, the current carried Dreams sideways back in the direction we’d just come, causing me to abort my docking operation in close proximity to one of the parties. The spectators in that boat—now almost close enough to step aboard Dreams—hastily grabbed their drinks in the event of a collision, but made no effort to assist. Fortunately, I avoided the other boats and on the third try I finally managed to correct for wind and current and made it into the slip, where, slightly embarrassed by my poor seamanship, I introduced myself to my new neighbors and promised to do better next time.

Tidal Forces

The tides are caused by balanced gravitational and centrifugal forces acting on large bodies of water—the same forces that maintain the moon in its orbit around the earth and the earth-moon system in its orbit around the sun. The tidal force can be visualized by imagining that a point in the center of the Pacific Ocean happens to lie directly beneath the moon. Here, at the point closest to the moon, the gravitational force of the moon is strongest, and the ocean surface will rise up, or “bulge” at this point, pulled by the moon’s gravitational force. On the opposite side on the earth, somewhere in the Indian Ocean, a similar bulge will be created. Since this point is more distant from the moon, the moon’s gravitational pull is weaker and no longer balances the centrifugal force. The unbalance allows water on the opposite side of the earth to bulge also.

If the oceans rise up on the opposite sides of the earth, it stands to reason that the ocean level will fall in other locations. For example, if we imagined the moon to be directly above a point on the equator at longitude zero degrees, and if the earth’s surface was uniformly covered with water, the drop in water level would occur at 90 degrees west and 90 degrees east longitude. In reality, the earth is not uniformly covered with water; the presence of the continents alters how the tides actually flow.

We know the earth rotates, and as it turns, the point closest to the moon also moves, meaning the “bulge” in the ocean travels as the earth turns. Consequently, an observer at a fixed point would see the ocean level first rise, then fall, and then rise again. However, as the earth rotates toward the east, the moon is also moving along in its orbit. Because of this, it takes slightly more than 24 hours—actually, 24 hours, 50 minutes—before that hypothetical spot in the Pacific Ocean is once again directly under the moon. This is why the high tide arrives around 50 minutes later each day at a given spot.

The sun also affects the tides. However, even though it is much larger than the moon—and therefore would be expected to exert a greater gravitational force—it is much farther away and thus the moon exerts the dominant effect. As the moon circles the earth every 29.5 days, it moves into and out of alignment between the earth and sun. During a new moon, both the moon and sun are on the same side of the earth and their tidal pulls combine to create high tides. A week later, when the moon is in its first quarter, it is 90 degrees out of alignment with the sun, and its maximum tidal pull tends to offset the sun’s minimum. At a full moon, the earth, moon, and sun are once again aligned on the same axis, with the earth in the middle, and high tides are again produced. When the moon is new or full, the tides are known as spring tides. Spring tides produce the greatest range of tidal swing, ranging from low water to high water. The careful observer, however, will note that there is a one to two day difference between the day of the new or full moon and the day of the highest tide; this is due to a phenomenon called the “age of the tide.” At one-quarter and three-quarter moons, the crests of the moon tides and the troughs of the sun tide tend to offset each other, and the swing between high and low tides is less than it is with spring tides. These tides are called neap tides.[34]

Finally, the position of the sun relative to the equator varies from summer to winter. At the summer solstice, the sun lies at an angle of 23.5 degrees north relative to the equator, producing the northern hemisphere’s summer. At the winter solstice, it lies at an angle of 23.5 degrees south. The angle of the sun relative to the equatorial plane  of the earth is called its declination. Knowledge of declination is one of the tools used in navigation. The moon likewise declines north and south relative to the equator. It is inclined 5 degrees relative to the earth-sun orbit so its declination varies between 28.5 degrees north and south. One effect of declination is to shift the mix of diurnal and semidiurnal tides. Another effect is the result of the fact that the orbits of the moon around the earth and the earth around the sun are elliptical, not circular. This means that at certain times the earth is closer to the moon and sun, while at other times it is more distant and the tidal force is less.

Fortunately, all of these movements—while difficult to visualize—are regular in nature due to the constancy of planetary movements within the solar system, and can be modeled and predicted years in advance by mathematical methods. Another complication emerges, however, and that is the effect of local conditions. Narrow inlets, shallow bays, irregular coastlines, the different sizes and volumes of the oceans and seas all affect the ultimate height of the tides at a given location. A good way to visualize this is to imagine the earth turning and the moon-induced “bulge” remaining fixed in place. As a shallow continental shelf is rotated under the bulge it acts as a wedge and raises the wave front.[35] Or, as the incoming tide enters a harbor or river that narrows, the level rises. For these reasons local measurements of tides are combined with the computer forecasts of planetary movements to construct accurate tide tables. The moon makes a complete swing of north-south declination each month, but requires 18.6 years to go through a complete cycle of its maximum declination. For this reason, data must be collected for 19 years to generate an accurate representation of the full range of tides at a given location. Once this is done, the data can be averaged to determine the mean tide level, sometimes called the mean sea level.  The mean sea level is defined as the average height of the surface of the sea for all stages of the tides over a 19-year period. This becomes the reference point for coastal or shore-based structures. For navigational purposes, it is more important to know the low water mark (to avoid running aground), so marine charts usually use the mean low water as a reference, and the depths of harbors or reefs are referenced to this level.

Types of Tides

Three types of tides can be observed: diurnal—one high and low tide each day; semidiurnal—two equal highs and lows each day; and a semidiurnal mixed tide. The last, as its name suggests, is a combination of diurnal and semidiurnal tides and differs from a straight semidiurnal tide in that the two highs are unequal as are the two lows. The Gulf of Mexico, northern Alaska, and parts of north Asia are examples of locations with diurnal tides. The East Coast of the United States, the west coast of Africa, Europe, and the west coast of Central America are predominantly semidiurnal. The U.S Pacific Coast, the Caribbean, and the west coast of South America are examples of semidiurnal mixed tides. All three types can occur in close proximity—as, for example, around the Gulf of St. Lawrence, Prince Edward Island, Nova Scotia, and the Bay of Fundy—although one type usually dominates.

The various crests and troughs of the tides are given the names of high water (HW) and low water (LW) for the highest and lowest points of diurnal and semidiurnal tides. In the case of semidiurnal mixed tides the nomenclature becomes more complicated because there are two crests and two troughs of different heights. They are referred to as higher high water (HHW) and lower high water (LHW), while lower low water (LLW) is used to distinguish the lowest low tide, and the higher low tide is called higher low water, abbreviated HLW. When the data are averaged as described in the preceding paragraph, the terminology becomes mean lower low water (MLLW), mean higher high water (MHHW), and so on.

Recall the grunion discussed in the preface. Survival of this diminutive fish is predicated upon its ability to know when the higher high water tide will occur. You might  wonder how it does this. Could it be that the grunion somehow senses the depth of the water and knows when the lows and highs are occurring? Or, does it surface at night to eye the size of the moon in anticipation of lovemaking on the beach? If so, it is probably not alone in this regard; other beachgoers have done this for ages.

Two examples of MLLW and MHHW come to mind. One summer Nancy and I in Dreams and our friends Tod and Linda White in Seascape (Refer to Chapter 5) set sail for a week of cruising—the goal being to circumnavigate Catalina Island, stopping and anchoring in various coves. One of the places I wanted to visit was a cove called Little Harbor. I had gone into it once briefly, just to see what it was like. The cove is divided into two parts by a jutting promontory of stone. A reef extends across about half of the opening to the cove. On the west side is the anchorage, with space for a half dozen boats, and on the east side of the promontory is a beach with breaking waves—the only spot on Catalina where surfing is possible. You enter the cove on the starboard or east side and once past the reef, turns to port for the anchorage, where the nominal depth is 2 to 3 fathoms (3.7 to 5.5 meters). The usual process is to swing in, drop a stern anchor in shallow water, and a bow anchor forward but behind the reef. After anchoring, I always dive the anchors to make certain they are set.

We accomplished this without incident and settled in to enjoy ourselves. As I recall, it was our turn to cook, so dinner was onboard Dreams. Before turning in, I checked the position and the depth once again. The boat had not moved and the fathometer read 2 fathoms. Dream’s draft is 1 fathom, so all was well.

At 5:00 A.M. (or “oh dark five hundred” as my navy friends like to say), I awoke instantly to the sound of a gentle bump. What was that, I wondered, sitting up in the bunk. A moment later it was repeated, this time a little more forcefully—enough to rattle the stays and shake the mast. I leaped out of bed and flipped on the fathometer. Sure enough, it read 1 fathom and we were hitting the bottom. I raced to the cockpit and threw some slack in the stern anchor rode, and used the windlass to pull the boat forward on the bow anchor. Fortunately I had plenty of scope out and could do that without a problem. Once I had 1.5 fathoms on the fathometer and everything secure, I tried to figure out what had happened. Then I realized the night before was MHHW—for the year. Correspondingly, when the tide went out and we encountered MLLW, it was negative, and the lowest depth of the year. At daybreak I dove under the boat and checked the keel. Fortunately we’d been lying in a sandy spot so no damage was done.

My memorable MHHW incident occurred about six months later, when the next highest annual tide occurred. The winter of 2004-2005 was unusual in Southern California in terms of heavy and continuous rainfall. Storm after storm rolled in from the Pacific or moved down from the northwest.  Newport’s beaches were littered with debris washed down the Santa Ana River and other streams that empty into the Pacific. At one point the beach was littered with large logs—where they came from I could not imagine. Floating offshore, they were a considerable hazard to any unwary fast-moving boat. The weather cleared briefly on New Year’s Day to permit a sunny Rose Parade in Pasadena, then turned stormy again. Rain fell more or less continuously during the second week in January. From Friday to Sunday alone, more than 7.6 centimeters (3 inches) of rain fell on Newport Beach. Beginning on Sunday, January 9, high tide conditions prevailed. However, because of the unremitting rainfall, continuous runoff into the bay, strong winds, and low pressure zone hanging overhead, the bay rose even higher, coming over low spots in the seawalls and flooding streets. On Monday, January 10, 2005, the tide peaked at a higher high tide of 2.2 meters (7.2 feet) according to my tide table. By Tuesday, January 11, the third day of the storm, the effective level in the bay approximated 2.5 meters (8.3 feet) at high tide, and the bay overflowed and flooded a good portion of the Balboa Peninsula, where I live. On my street, water slowly rose to the level of the curbs and then overflowed into the gardens and front yards of my house and neighboring houses. Fortunately, the water did not enter the house, but it did remain high for several hours before draining back into the bay. I interrupted my writing on this book long enough to survey the scene and take some photographs, wading barefoot in the river of saltwater that ran down the street. One of my neighbors, Bob Wilson, interjected some humor in an otherwise tense moment by launching a surf board down the street—his very nervous dog onboard. Other neighbors joked about owning waterfront property.

We were fortunate; other homes in Southern California sustained major damage during the January storms. But the experience brought home the significance of storm surges and the potential for loss and damage they create, particularly when combined with an unusually high tide.

Tide Waves

As I mentioned at the start of this chapter, tidal changes act as a long wavelength wave. Since this wave has a long period, its speed is determined by the depth of the water and can reach as high as 370 knots. The tide wave can move across an ocean until it hits the opposite shore, where it can be reflected or refracted or standing waves can be established in ocean basins. Scientists have measured tidal heights in the open ocean, although the change of tides is more easily seen near shores. The position of the high tide moves in a known manner, so if the tide is measured at one coastal location, it can be predicted for nearby locations. For example, if the high tide on the west coast of central Mexico occurs at midnight, it will be high tide near the tip of Baja California two hours later, San Diego, about three hours later, Santa Barbara, four hours later, and Alaska eight hours later. Yet, in the western North Pacific Ocean, high tide occurs at the same hour along a vast arc extending from Japan south to New Zealand. This can be seen from lines of position where the high tide occurs at the same time in the major oceans; these are known as cotidal lines.[36] Why is this?

In a large ocean basin the tide wave moves across the basin as a progressive tide. When the wave reaches the shore, it is reflected back, but if the basin dimensions are large compared to the wavelength, no standing wave is created. In a smaller ocean basin, the dimensions can be such that the basin’s natural period equals the tidal period of 12.42 hours (semidiurnal) or 24.83 hours (diurnal). When this is the case, a standing wave can be produced. This is the situation in the northeastern and southwestern Pacific and in the North Atlantic Ocean. Because the standing wave travels a long distance, the Coriolis force has an effect on the moving water, turning it slightly in a clockwise direction (northern hemisphere) and counterclockwise in the southern hemisphere. This is called a rotary tide wave. The movement causes the high tide crest to rotate counterclockwise around the basin while the tidal current itself rotates clockwise. Picture a bicycle wheel lying flat on a map of the Pacific Ocean, its axle (center) near the Hawaiian Islands and its rim touching the west coast of North America. Imagine the wheel rotating counter clockwise; the movement of the spokes will simulate the movement of the high tide crest.

In narrow bays, fiords, or channels open at one end to the sea, it is possible for the natural period of the bay to resonate with the tidal period. The classic case of this is the Bay of Fundy between Nova Scotia and New Brunswick, some 90 nautical miles long. At the entrance of the bay the tidal range is between plus and minus 1 meter (+/- 3.3 feet), but at the head of the bay it is between plus and minus 7 meters (+/- 23 feet).

Seiching

Following one of Southern California’s earthquakes, I noted that some of the water had splashed out of a neighbor’s swimming pool. When I inquired as to how this had happened, he described a series of waves created during the earthquake. This phenomenon is known as seiching and can occur when any external force disturbs an enclosed body of water. Waves move back and forth from one end to the other. The period of the waves depends on the size (length and depth) of the body of water. (See Appendix 1 for typical calculations.) In this sense they can also be described as standing waves. Seiches can be caused in bays and harbors by tidal currents, by the arrival of a distant swell with just the right period, or by storms or a tsunami. Sometimes these will oscillate for days.[37] Seiches are generally not a problem and are detectable only by means of careful measurements. However, in the case of harbor designs, one usually studies the predominant wave periods in the area and ensures that the harbor dimensions do not create a condition where large seiches can occur, since this could cause excessive movement of floating docks and straining of vessel mooring lines.

Hurricane Katrina (August 29, 2005) caused an 8 meter (26 foot) storm surge. This raised the level of Lake Pontchartrain enough to damage the levees and flood New Orleans. It also caused a rotating seich that lasted for several days.[38]

On a large scale, seiches have proved dangerous, damaging boats at dock, and occasionally killing people fishing near shores or on breakwaters. Such an incident occurred on June 26, 1954, when a 3 meter (10 foot) high wave suddenly rolled in from Lake Michigan and swept eight fishermen off of a breakwater, drowning them.[39]

A seich requires some exciting force. On the Great Lakes, seiches are caused by fast moving thunderstorms or squall lines that move eastward across the lake. The combination of the wind blowing toward a low pressure area enables a wave to form. In deep water, the wave is not very high. With the right wind speed and direction, the squall line can move as fast as the wave front, literally pushing it ahead. As the wave approaches shallow water near the shore, its height increases, governed by the same physics as any other wave. After hitting the Michigan side of the lake, the wave is reflected back toward the Illinois side. This is where its insidious nature becomes evident. If the originating storm was fairly short-lived, the chances are that the lake has returned to normal on the Illinois side; boaters and others may have resumed their activities in the aftermath of the storm. Suddenly, out of nowhere, a wave can appear and disrupt the scene. In 35 years, there have been five major seiches that have caused damage along the Chicago lakefront. During the summer of 1988 there were three noteworthy seiches along the Chicago lakeshore. These were not as bad as the one in 1954, but some damage resulted. They caused the water level to rise or fall by as much as 0.3 to 1.2 meters (1 to 4 feet), in some cases with the change occurring in less than 10 minutes. Boats can drop and hit bottom, or if dock lines are snug, the lines can break or rip cleats out of the boat or off the dock.

Tidal Bores

Tides in general do not create extreme waves. Tidal currents in the open ocean are weak—say, 0.1 to 0.2 knots—but near the coast or in bays and river mouths they can reach 5 knots or more. In shallow rivers, when currents exceed a critical speed (c> (gD)0.5), tidal bores appear.[40] This is one tidal phenomenon that can create unusual if not large waves—a wave that moves forward as a wall of water.

If large tides occur in narrow harbors or river mouths, the rapidly changing height of the water is compressed into a narrow channel, the current flowing much faster than the current of the tide wave in the open ocean. This can cause a fast moving wave to sweep up the channel, sometimes creating hazardous conditions for boats entering or leaving the area. The wave can be a breaking wave or just an abrupt wave front; it is called a tidal bore. Usually tidal bores are around 1 meter (3.3 feet) in height, but can be as high as 8 meters (26 feet) —for example, on the Qiantang River in China. Plate 6 (See book) is a photograph of the Qiantang bore taken in late August 1986, from a location near the city of Hangzhou. The bore forms below the city and then travels at the rate of 10 to 20 knots up stream for about 25 miles. In September and October visitors arrive from all over China to watch the spectacle. A number have ventured too close and have been swept to their deaths. Local boatmen know to get their vessels out of the way!

Plate 6: The Qiantang River Tidal Bore

The Bay of Fundy, described above, was once known for a tidal bore but has been modified by construction of a causeway.[41] Other notable tidal bores occur at Turnagain Arm of Cook Inlet, Alaska, with a difference of 9.2 meters (30 feet), the Severn River, in England (a series of waves about 0.3 meters (1 foot) high, the Seine River, and the Amazon River.[42]

I had my first view of the Amazon River many years ago, at Belem, a wonderful city near the mouth of the river. At the time I was impressed with the Amazon’s tremendous size and the variety of tropical plants and wildlife. I walked along the waterfront, where Indians from upriver came to the feira (marketplace) to sell goods—wild animals, snake skins, various herbs and remedies, bananas, and dozens of tropical fruits totally unknown to me. I heard the stories about this tremendous river—how it flowed out into the Atlantic with such force that fresh water could be found 50 nautical miles or more distant from land. A local legend told of shipwrecked sailors, on the verge of dying of thirst, who, in their final hours of desperation started to drink saltwater—only to discover it was fresh water. They were far from shore, but in the outflow of the Amazon River.

Later I visited Manaus, 1,450 kilometers upriver from the Atlantic Ocean. Flying west, the river was so wide that looking down from the windows of the airplane, I could not see both banks at once. There are floating docks in Manaus—designed for the huge rise and fall of the river, from the rainy (flood) season to the dry season. If memory serves me correctly, this fluctuation is 12 to 15 meters or more. I’ve not seen the tidal bore on the Amazon. Bascom says it is spectacular and attains a height of 7.6 meters in some locations. It travels upriver at a speed of 12 knots for a distance 480 kilometers.[43]

Given what I know about the river, it sounds plausible to me, and a good reason to return there and check it out. Perhaps I could get Eric Akiskalian, Dan Moore, and some of the other extreme surfers to join me; it would be the longest ride of their lives!

From Chapter 10

Additional details regarding the growth of container ships

There are three east-west principal trade routes used by container vessels as well as a half a dozen secondary routes. The main routes are the transpacific (Asia-North America), Asia-Europe, and Europe-North America. The highest volume route is the transpacific, where cargo volume has tripled between 1990 and 2004.[44] During this time, the number of containers carried increased from 3 million to nearly 10 million TEUs. The Asia-Europe route has about one-half as much traffic; the transatlantic, about one-fifth as much.

This increase in container transport volume is the result of several factors: a doubling of the weekly sailings, faster vessels, and an increase in the average vessel size. The average speed has increased from around 19 knots in 1990, to 23 to 24 knots in 2004, and may reach 25 knots in the next decade.[45] Also, electronic transfer of documents and payments has had an impact.

Industry practice is to measure capacity in terms of an equivalent number of 6.1 meter (20 feet) long containers transported. They have been the industry standard for years, but today they are being supplanted by containers 12.2 meters (40 feet) long. There are also refrigerated containers, typically 13.7 meters (45 feet) long. Capacity of typical containers is shown below:

Type:                                                                20 feet (1 TEU)            40 feet (2 TEU)

Length, meters (feet)                                         6.1 (20)                        12.2 (40)

Height, meters (feet)                                         2.6 (8.5)                       2.6 (8.5)*

Width, meters (feet)                                          2.4 (8.0)                       2.4 (8.0)

Gross weight, kilograms (pounds)                     30,480 (67,056)           30,480 (67,056)

Tare weight, kilograms (pounds)                       2,240 (4,928)               3,950 (8,690)

Volume, cubic meters (cubic feet)                     33.2 (1,173)                 67.5 (2,383)*

* Some are 2.9 meters (9.5 feet) high and have a volume of 76.4 cubic meters (2,695 cubic feet)

Loaded to capacity, a single container can thus hold 30 metric tons (33.5 short tons) of goods. Even an empty container weighs 2.2 to 4 metric tons (2.5 to 4.3 short tons). From these dimensions, one can readily imagine the danger if a container is lost overboard during a storm. Collisions between small vessels and a floating, partially submerged container have resulted in the sinking of vessels

Average vessel capacity on the transpacific route is expected to continue to increase, from 3,900 TEUs to around 5,800 TEUs by the year 2020. Within the next decade even larger vessels are expected. New container ships will carry 6,000 to 8,000 TEUs or more. The motivation for larger vessels is economic; the shipping cost per container is expected to drop by \$100 per TEU for an 8,000 TEU vessel and by \$150 for a futuristic12,000 TEU vessel. Looking at new ship orders within the next five years, 750 new container vessels will be procured. About 500 of these will be Panamax size or smaller, typically 2,500 to 5,000 TEU capacities, while 250 will be “post-Panamax,” with capacities of 5,000 to more than 8,000 TEUs. Of the latter, nearly 50 percent are more than 8,000 TEUs and range in length from 900 to 1,150 feet.

From Chapter 10:

Analysis of the Derbyshire Hatch Cover Failure

The hatch covers were apparently designed for a uniform static wave load of 17,200 Pascals (1.75 metric tons per square meter or 358 pounds per square foot).[46] Since seawater has a density of 1.028 metric tons per cubic meter, this design criterion is equivalent to the load imposed by a column of water 1.7 meters (5.6 feet) high on top of the hatch covers. The Derbyshire’s freeboard was 6.9 meters and the coaming height was 2.0 meters, so the total height of the hatch cover above the water line was 8.9 meters (29.2 feet). Hence, a wave 8.9 + 1.7 meters (5.6 + 29.2 feet) high, or 10.6 meters overall height, would be high enough to go over the rail, cover the hatch, and cause the design loading to occur.

Recognizing that the design incorporates some safety factor, the next question is: “At what load does total collapse of a hatch cover occur?” When this analysis was carried out, the result was a static loading 5.3 meters (17.4 feet) high.[47] This corresponds to a wave 8.9 + 5.3 meters (29.2 + 17.4 feet), or 14.2 meters (46.6 feet) high.

In addition to failure caused by the dead weight of tons of water on the hatch cover, it could also fail under dynamic loading as well. In other words, as mountainous waves crash down on the hatch cover, the impact causes a sharp pressure impulse, something ship designers call a Gifle peak. This sudden pressure pulse (analogous to the sudden rise in pressure caused by an explosion) can produce stresses 11.6 times greater than those caused by the static load, leading to brittle fracture of the steel. This type of fracture was observed in the Derbyshire’s wreckage.[48] Unfortunately, bulk carrier design standards have no requirement to consider dynamic loading.

Finally, how high were the waves experienced by Derbyshire? We do not know with certainty, although typhoon Orchid’s reported wave heights in the vicinity were 18.3-plus meters (60-plus feet). The height can be estimated on the basis of an energy spectrum assumed for the storm depending on its duration. Assuming the storm lasted 6 hours, this analysis indicates that the probability of waves higher than 22 meters (72 feet) is 100 percent, higher than 24 meters (79 feet), 99 percent, and higher than 26 meters (85 feet), 80 percent.[49]

Appendix 1: Wave Mathematics and Ship Design

(This is the complete version of the Appendix)

The purpose of this appendix is to provide additional details for readers who are interested in understanding some of the theory behind extreme waves and how they affect ships. It can be safely ignored by the general reader who has already suffered through enough mathematics in the text.

Mathematics of the Simple Wave

First, recall the admonition first expressed in chapter 1—namely, that the actual sea surface is a complex of many waves of varying sizes, coming from different directions and having different periods. Only in the case of a calm sea, with a single low swell, do the waves even remotely resemble the ideal wave shown in figure A-1. The speed of waves depends on the depth of the water in comparison to the wavelength. In the open ocean, the size of waves depends on the exciting force (usually the wind); water depth is not a factor until the wave reaches shallow water. In attempting to deal with the complications presented by the actual sea state, analysts have developed various linear models, each having applicability over a certain range of conditions. Recognizing the limitations that linear models have in representing complex seas, statistical (probabilistic) models have been developed.

In efforts to further improve analytical models, analysts have developed nonlinear mathematical models with the goal of better modeling realistic waves and ultimately forecasting their occurrence. Each method offers certain advantages in comparison to the others; none have proved to be completely satisfactory.

To better understand some of the theory behind linear wave analysis, we begin with the sine wave, a simple waveform that occurs frequently in nature and that is common to many fields of physics, including electricity, light, and sound. The most common everyday example of a sine wave is the alternating electric current found in every household with electric power. The shape of this wave is illustrated below. As can be seen, starting on the left hand side the wave has a crest, then the amplitude gradually falls to zero on the center line horizontal axis, decreases to a negative crest, or trough, and then returns to a maximum value again after crossing the center line. In the home, the frequency f of the sine wave is 60 cycles per second (50 cycles per second in Europe and many countries), the period T of the wave is 1/60 second or 16.7 milliseconds. Period is the reciprocal of frequency, that is, T =1/f. With waves, the period, not the frequency is the term normally used.

Figure A-1: Wave Nomenclature

For ocean waves, H is called the wave height (the difference in surface elevation from the crest of one wave to the successive trough). In addition, the time elapsed for one complete cycle of a wave—that is, from one crest to the next—is called the period T. The wavelength L of waves in deep water is related to the period T.

In deep water, defined as water in which the water depth D is equal to or greater than one-half the length of the wave—that is, where:

Depth D > 0.5L, where D is the water depth in meters and L the wavelength, both in meters, the wavelength of the ideal wave is given by [1]: [50]

Wavelength L (meters) = (g/2π) T2                                [1]

where g is the acceleration due to gravity,  9.81 m/sec2, T is the period in seconds, and π = 3.1416.

Also,

Wavelength L (meters) = cT                                         [2]

where c is wave speed in meters per second.

Equations [1] and [2] can be simplified to the following forms:

Wavelength L (meters) = 1.56 T2 where T is the period in seconds

Speed c (meters/second) = 1.25 L0.5 = 1.56 T

Period T (seconds) = 1/f where f is the frequency in cycles per second

Making use of these formulas, we can compute the following values for typical idealized waves (all numbers are rounded):

Period, T, seconds                    2          4          6          8          10        15        20

Wavelength L, meters   6          25        56        100      160      350      620

Speed c, meters/second            3          6          9          12        16        23        31

The speed of the wave is independent of depth and is determined only by the period, as noted above.

Conversely, in shallow water, defined as water where the depth is 1/25th or less of the wavelength, or where:

Depth D < L/25, where D is the water depth in meters and L is the wavelength.

The speed of the wave depends on the depth in accordance with the following relationship:

Speed c, meters/second = (gD)0.5                                             [3]

where g is the acceleration due to gravity, 9.81 meters/second squared and D is the depth in meters, as noted before.

Wave steepness is another parameter of interest to us. It is defined as the ratio of the height of the wave to the wavelength:

S (steepness) = wave height H/ wavelength L

Using [2], the equation for wavelength, the steepness of an ideal wave can be calculated as follows:

S (steepness) = (2π H)/gT2                                                       [4]

The theoretical upper limit on steepness is that point at which the wave becomes so steep that it breaks. This has been calculated to correspond to a steepness of 1/7 = 0.14.[51] The typical range of steepness for waves in deep water is around 0.01 to 0.1. If the steepness of the Draupner extreme wave shown in figure 24 is analyzed, it is about 0.059, whereas the steepness of the significant waves in that same record is 0.027.

Extreme waves are not only very steep, but typically they are asymmetrical. In a symmetrical wave, the height of the crest from the center of the wave would be the same as the distance from the center of the wave to the bottom of the trough. In other words, the crest height would be equal to 0.5 times the wave height. In extreme waves we find that this ratio can be 0.7 or higher. In the Draupner wave mentioned above, the crest height was 18.5 meters and the overall height was 25.59 meters, giving a ratio of 0.72.

How Did Ramapo Determine the Wave Height?

Figure A-2 shows the geometry of the vessel as it encountered heavy seas. (Refer also to chapter 8 for a discussion.) I assume the officer on the bridge of the Ramapo had or could easily measure the following distances: d1, d2, and d3, the horizontal distances from the stern to the mast, from the mast to the bridge, and from the bridge to the bow, respectively. Also recognize that d1 + d2, + d3 = Ls, the length of the ship, or 146 meters. The height of the crow’s nest hc and the height of the bridge hb were also known. The angle of the ship θ and the distance to the projected line of sight “x,” and the wave height hw are unknown.

Figure A-2: USS Ramapo Height Measurement Model

The first step is to solve for “x” using similar triangles. We find:

x = [hb(d2 + d3) –hcd3]/(hc-hb).

Next, find θ by trigonometry:

θ = sin-1[hc/(d2 + d3 + x)]

Finally, find hw by similar triangles and trigonometry:

hw = (146 + x)sin θ = 34.2 meters (112 feet)

Tsunami

Since tsunami have very long wavelengths relative to the ocean’s depth, the velocity of a theoretical, sinusoidal tsunami wave is given by [3], that is:

Tsunami wave speed c (meters/second) = (gD)0.5

Using this formula and the average depth of the ocean, or 4,000 meters (13,115 feet), we see that a tsunami travels at around 198 meters per second (713 kilometers or 442 miles per hour). In deep water, a tsunami can travel faster than the commercial jets carrying passengers to Hawaii. The periods are typically 10 to 20 minutes but can be as long as an hour. Since the wavelength is a function of wave speed and period, (L = cT, equation [2]), we can estimate that wavelengths are typically in the range of 120 to 240 kilometers (74 to 148 miles).

The above relations do not hold when the tsunami moves into shallow water. In this case, for shallow water where the depth is between 0.5L and 0.04L, the tsunami wave speed is given by:

Tsunami wave speed c meters/second) = {(gL/2π)[tanh(2πD/L)]}0.5      [5]

When the wave reaches shore, it increases in height in shallow water and then runs up on land as indicated in figure 18. The maximum height of the run-up can be estimated as:[52]

Maximum run-up height Hmax meters = k(cot α)0.5 Hs1.25                         [6]

In this equation α is the slope of the seabed in degrees as the wave approaches shore, Hs is the wave height at shore or the toe of the beach, and k is a constant depending on the wave type. For a continental shelf, α could be as small as 0.1 degrees and 1 to 10 degrees for a beach. If the wave is a solitary wave, k is 2.83 but if the wave is preceded by a trough, k is 3.86 and if it is a double wave (a large wave preceded by a small wave, then a trough), k is 4.55. For a beach sloping 1 degree, an incident double wave of height 0.5 meters would experience a run-up of 14.4 meters (47 feet).

Tsunami can cause seiches in harbors and bays if the wave period is close to the natural period of the bay or an even fraction (1/2 or ¼) or an even multiple of the period. It is this phenomenon that led to the name tsunami (Japanese for harbor waves) when sailors observed that waves continued rocking the harbor long after the earthquake had stopped. An approximate equation for the period is given by:

Closed harbor or bay, period T in seconds = 2Lh(gD)-0.5                                   [7]

Open harbor or bay, period T in seconds = 4Lh(gD)-0.5

Here Lh is the length of the harbor or bay in meters, D is the depth in meters, and g is the acceleration due to gravity, 9.81 meters/second.[53] A “closed” harbor is one surrounded by a breakwater and having a narrow entrance. Real harbors and bays have complicated geometries and these equations may not give accurate results. Newport Harbor (figure 23) is an example of an open harbor. Assuming an average depth of 3 fathoms (5.5 meters), and a length of 5,100 meters, the period of Newport using [7] is around 2,775 seconds or 46 minutes. The period of Hilo Bay is around 30 minutes; the predominant period of the April 1, 1946 tsunami was 15 minutes, which was one of the reasons it was so devastating at Hilo. The period of the Bay of Fundy is 13.3 hours—very close to the period of the semidiurnal tides. This explains why the tidal range is between plus and minus 1 meter high (+/- 3.3 feet) at the entrance and yet between plus and minus 7 meters (+/- 23 feet) at the head of the bay. Research has shown that this period arises from the combined system of the Gulf of Maine with its deep water and the shallow depth of the bay.[54]

The above relations are chiefly useful in that they provide insight into the physical parameters (wavelength, period, and ocean depth) and how they affect wave propagation and height. As mentioned in chapter 1, realistic ocean conditions are more complicated. For example, run-up calculations are actually more complicated because realistic shore conditions are never uniform. Likewise, the periods of bays are affected by their width and of course the depth is not uniform. In an effort to better model real waves, theoreticians have developed more complex nonlinear models, and then turned to numerical methods using digital computers to simulate wave motions. Entire books are available on this subject, and details are beyond the scope of this book.[55]

In chapter 3 the topic of wave probabilities was introduced. Probabilities are developed using a statistical approach that assumes that the sea state satisfies certain criteria for randomness. This approach has many practical applications and is in wide use, even though it does not meet the requirements for forecasting extreme waves. It is particularly useful for the design of structures.

Researchers have used recorded wave height and period data (using a large number of records) to construct wave energy spectra. These are based on the principle that the wave energy is proportional to the square of the wave height. Typical spectra graphs have a parameter called the spectral density (related to the wave energy) on the vertical axis and period or frequency on the horizontal axis. Model spectra are for deep water (fully developed seas) and one for fetch-limited seas, called the Joint North Sea Wave Project (JONSWAP) spectrum. These spectra can be modified for a given location or for a given sea condition to make them specific for a given purpose. They can also be used for hindcasting, in other words, back-tracking from a recorded wave spectrum to come up with an estimate of wave heights, average period, and average wavelength.[56]

Earlier I stated that the use of linear theory and Gaussian models requires a number of assumptions that are invalid in realistic seas. For example, real waves are slightly nonlinear in deep water and very definitely nonlinear in shallow water. This can be seen by considering asymmetry (high crests, shallow troughs) and the fact that crests can be steep and troughs flat.[57]

To better represent extreme waves, the Weibull probability function has been used. (The Rayleigh distribution is a special case of the Weibull distribution.) The assumption is made that the wave data represent a stationary sea state between measurements. The Weibull distribution provides a good fit to the Draupner extreme wave shown in figure 24, and thus may be a useful tool for understanding some aspects of sea conditions (such as sea state duration) leading to the formation of extreme waves.[58]

Recent Research on Extreme Wave Models

As awareness of extreme waves has grown, researchers intensified efforts to understand the physics underlying their formation. If the occurrence of extreme waves can be linked to certain meteorological or sea state conditions, then it might be possible to forecast when they will occur. Such information would be invaluable to mariners and the marine insurance industry.

Much of what we know about extreme waves—indeed, the emphasis to learn more about them—has come from observations by shipmasters who have witnessed encounters between their vessel and an extreme wave or from survivors of vessels that foundered as a result of an extreme wave incident. Those observations are by their nature imprecise; generally they occurred too suddenly or under extremely stressful conditions where exact measurements were impossible.

In chapter 8, I grouped them by characteristic probable cause, in the following order:

• Strong currents
• Storms
• Continental shelves and shallow seas
• Constructive interference (superposition)

To these we may add several additional possible mechanisms for extreme wave formation that are the subject of current research:

• Nonlinear effects
• Spatial or temporal focusing effects
• Multidirectional effects
• Modulation and resonance

A comment or two about each of these mechanisms is useful. The first category, strong currents, has indisputably been the source of extreme waves. When swell or storm waves encounter a fast-moving opposing current such as the Agulhas Current or the Gulf Stream, they tend to “pile up” as their velocity is reduced. Professor Garrett pointed out that a wave with a phase speed of c meters per second can be stopped by an opposing current of only ¼ c.[59] When this happens, steep, high waves result, proceeded or followed by deep troughs. Thus the evidence is clear that the probability of encountering an extreme wave is greater under these conditions and a prudent mariner should avoid this situation if possible.

The increase in wave size as a function of wind velocity, fetch, and wind duration is a well-known phenomenon in storms. There are correlations that provide estimates of the significant wave heights under varying storm conditions, but none that predict the random occurrence of extreme waves. This suggests that some additional mechanism, yet to be fully understood, is at work. It would be useful to know if extreme wave formation is governed by a threshold effect; in other words, do seas have to build to a certain point before extreme waves are produced? Or, is it purely a statistical effect?

The evidence seems to indicate the latter possibility, because many mariners (myself included) recall sailing in relatively calm seas where the significant wave height was one meter (a few feet) or less, but suddenly a wave two to three times as high struck the vessel.

Likewise, shallow water, bottom effects, and refraction, have the effect of slowing waves and causing wave heights to increase. Thus areas where there is a sharp transition in the sea depth are potential danger zones in rough seas. The question here is: “Are there certain sea or wind conditions that combine to cause an extreme wave and how can they be anticipated?”

Constructive interference, (sometimes called superposition) is the fourth category mentioned in chapter 8. Here I included incidents (to the best of my knowledge) in which an extreme wave struck a vessel in the absence of the other conditions described above. Superposition is a well-known phenomenon, observable in many areas of physics, so its existence is not in doubt. The relevant research question is whether or not it is capable of causing waves that are 2.2-2.4 times as high as the significant wave. From the Rayleigh distribution, the answer would seem to be yes. (A factor of two seems obvious.)

Turning to the new areas of research, attempts to model nonlinear wave effects may shed light on how superposition can produce extreme waves. Nonlinearity makes mathematical modeling much more difficult, so scientists and engineers always try to develop linear models first and then turn to nonlinear models as a last resort.

In case you, the reader, are not a mathematician, scientist, or engineer, but have bravely ventured into this appendix to further your understanding, let me offer a simple example that will hopefully ease the pain of wading through successive paragraphs of this section.

Consider a steel bar—say, a familiar piece of reinforcing steel. Imagine that it is put in a tensile test machine, a machine that grasps both ends of the bar and pulls on them. Suppose the machine is set to pull with a certain force, and as a result the bar stretches a small distance we will call “x.” Now, if the force is doubled, the bar elongates a greater distance, this time equal to twice x, or “2x.” If the force is tripled, the elongation becomes 3x, and so on. In technical terms, we have discovered that strain (elongation) is directly proportional to stress (applied force).[60] In other words, the bar is acting as a linear system—double one variable, the effect doubles.

However, if we keep increasing the force indefinitely we know that at some point the bar will break. If the force is increased carefully and slowly, what we observe is that the bar reaches a point at which elongation more than doubles when the force is doubled. In technical terms, the steel has been stretched beyond the elastic limit.

Up to the elastic limit, the bar behaves like a tight rubber band—remove the force, and it shrinks back to its original length. This is another characteristic of a linear system. Once beyond the elastic limit, the bar is permanently deformed. There no longer is a simple one-to-one relationship between stress and strain; the bar now behaves as a nonlinear system. Mathematically we say that “higher order terms” must be brought into the equation to give accurate results. Let me next explain what this means.

In the linear (elastic) region, elongation is proportional to the applied force, so we can write:

e = kf                                                   [8]

where e is elongation, in millimeters or inches, k is a constant, and f is the applied force. Now, once the bar passes the yield point, the equation has to be written differently, and might take a form like this:

e = kf + k1f2                                         [9]

Here, k1 is another constant. Note the exponent “2” on the second term of the equation. This means that the square of the force has come into the picture. Whenever one of the variables is squared or cubed, or increased to the nth power, it is said to be a “higher order” term in the equation. These higher order terms seem to be simple in appearance, but they give mathematicians headaches when it comes to solving equations.

Back to extreme waves. Some new research is directed at examining the effects of second order and higher terms in mathematical models of waves, to see if this is a better way of modeling waves. Some researchers go so far as to say that if rogue waves exist, they must inherently be nonlinear.[61] Some of the features of extreme waves—their steepness and shape of the wave crest—are modeled more accurately when second-order terms are included.

Another interesting new approach is based on spatial and temporal focusing. Spatial focusing is another way of describing what happens when waves are refracted by the ocean bottom topography in coastal waters or by current gradients.[62]Temporal focusing may result when waves disperse. Some wave groups may contract to a few wavelengths and then combine with others to produce short groups of very large waves.[63] Some theorists believe that nonlinear focusing may allow a wave to “borrow” energy from its neighbors, becoming as much as 4.5 to 5 times as large as the average wave height.[64]

Multidirectional and multidimensional effects are also being studied to see if they can cause extreme waves. The idea is to investigate if extreme waves result from wave trains interacting at an angle, or due to three-dimensional interactions—effects that would not be modeled by a one-dimensional analysis. When I spoke with Dr. Susanne Lehner, she indicated that waves from crossing seas arriving from two different storms can add and build to an extreme size due to the continuous input of energy. Also, the Benjamin-Feir index, introduced in chapter 11, measures a phenomenon called the Benjamin-Feir instability. It is defined as the ratio of the mean square slope of the frequency spectrum peak to its normalized width. Under the right conditions, instability causes the wave train to break up into periodic groups. Within each group a further focusing takes place, producing a very large and steep wave having a height roughly three times the initial height of the wave train.[65]

Finally, other research is directed at seeing whether frequency or amplitude modulation could be responsible for extreme waves. Or, is it possible that certain wave periods and frequencies will resonate with a given sea-state condition to create extreme waves. The analogy to this is easily demonstrated in a bathtub. A bathtub, or a harbor for that matter, has a series of resonant frequencies. See equation [7] above. If you take a piece of wood (or possibly just your hand) and get the water sloshing back and forth at just the right period, a large wave will occur.

Given that waves as high as 30.5 meters (100 feet) exist and occur more frequently than previously known, what are the implications for ship design? To answer this question, I consulted with Captain Jerry Fee, USN (ret).

Waves and Ship Design

Captain Fee kindly gave me a short course on the process the United States Navy uses to design ships. The approach used in commercial shipping is similar, although some of the design criteria differ. According to Captain Fee, the primary stresses in a ship are determined by an analysis based on hogging or sagging, using an assumed wave height (in feet) given by:

H = 1.1 (Ls)0.5                                                                         [10]

where Ls is the length of the ship in feet. Thus, for a vessel 900 feet long, the design wave height would be (1.1)(30) = 33 feet high. Note: Converting the formula to metric units it becomes H = 0.61 (Ls)0.5, where now H and Ls are in meters. Historically, the U.S. Navy has taken the position that the largest wave likely to be encountered was 21.4 meters (70 feet.) Based on more recent experiences the navy now believes that larger waves can occur, but that they are unstable and only last for a brief period. The possibility of extreme waves that are steeper and possibly do not have longer wavelengths is now recognized.

Powerful computer programs using a method called finite element analysis calculate the primary stresses in the ship’s ribs, longitudinals, and other main structural elements, to ensure that the sizing of steel members is adequate for the expected loads. The navy’s general criterion is built around a Sea State 8 condition. In Sea State 8, the average 1/3 highest wave is about 14 meters (45 feet). This is typical for most hurricanes. Hurricane Camille is one of the best recorded hurricanes, and the navy uses a wave scenario based on this hurricane in their ship models to check for dynamic stability and survivability. On the basis of other analyses, the navy has not had to make any fundamental changes in ship design as a result of the prospect of a wave greater than 21.4 meters (70 feet). Naval vessels appear to already have sufficient strength built into them to survive an encounter with a larger wave using the existing criteria since maximum hogging and sagging loads are encountered when a ship is caught between two large waves whose wavelengths equals the length of the ship.

The energy carried by a wave is proportional to the square of its height. For this reason, a 30.5 meter (100 foot) high wave will hit a vessel with four times the force of a 15 meter (50 foot) high wave. If a high wave is traveling at 35 knots and a vessel traveling at 20 knots runs into it bow first, the combined velocity of the impact is 55 knots. The resulting slamming force can stress the bow structure.

Consequently, other parts of the ship structure that may be subject to wave forces are also examined to ensure that they are sufficiently strong to resist the forces that will occur. The next step is the design of the deck plate for “deck wetness.” Those areas subject to extreme deck wetness are the bow area and parts of the superstructure that encounter extreme wave loading due to wave slap and the dynamic load of large amounts of water pouring onto the deck in an extreme wave encounter.  The basic design criterion is to assume a pressure of 24 kilopascal (500 pounds per square foot) for any area that is prone to “green water” (wave slap). Most navy vessels are designed for at least 71.9 kilopascal (1500 pounds per square foot), and some unique parts of a structure, such as the sponsons on an aircraft carrier, are designed for as high as 359 kilopascal (7,500 pounds per square foot). In addition, a static head equivalent to a column of green water 2.4 to 3.1 meters (8 to 10 feet) high, is designed in the forward part of the vessel that is likely to encounter waves. This is reduced linearly as you move aft from the bow of the vessel where a value of 30.6 kilopascal (640 pounds per square foot) is used to a minimum value of 1.2 meters (4 feet) of head, equivalent to about 12.3 kilopascal (256 pounds per square foot). Military vessels include additional design conservatism to account for the need to resist blast over pressure during combat operations.

Both military and commercial vessels are designed to stay afloat with one or more hull compartments flooded. In the case of commercial vessels, one or two flooded compartments is the norm, while for the navy it is three.

The military has progressed from using steel with a yield strength of 207 to 276 megapascal (30,000 to 40,000 pounds per square inch) called HTS or high strength steel to using high yield strength steels (called HY steels) that have a yield strength of 551 megapascal (80,000 pounds per square inch). Submarines use 714 megapascal (100,000 pounds per square inch) HY steel. The norm for commercial ships is HTS at 276 megapascal (40,000 pounds per square inch). Further verification of ship designs is accomplished by carrying out model tests in wave tanks. Once the vessel is commissioned, it will undergo sea trials to verify performance and operational characteristics.

As the navy’s top ship designer, Captain Fee took part in numerous sea trials. When he served as the Aegis shipbuilding program manager, he took part in an interesting one. It was an Aegis-Class cruiser that went to sea in February 1986, at a time when a strong northeast storm had been blowing for several days with 50 knot winds. Waves were around 12 to 15 meters (40 to 50 feet) high. Fee ordered the ship to head into the waves at 30 knots, as opposed to the normal practice of slowing down. After several hours the experiment had to be terminated, because the air intakes 26 meters (85 feet) above the water line were being blocked by ice formation! Incidentally, the ship suffered only minor damage.

Current maritime design practice for commercial vessels varies with the classification societies and is based on withstanding the impact of an idealized (symmetrical) wave 10 to 15 meters (32 to 49 feet) high. The water in such a wave exerts a static pressure of 49 to 75 kilopascal (1,024 to 1,568 pounds per square foot) on the side of a hull and twice this amount if the total weight is on a horizontal surface. The dynamic pressure is greater and depends on the wave velocity:

Pressure P in Pascal = ½ Ccρc2                         [11]

Here Cc is a load concentration factor, taken as 3 for global impacts and as 9 or 10 for local impacts where the wave force is concentrated, ρ is the density of salt water and c is the velocity of the wave crest in meters per second.[66] Extreme waves with heights of 15 to 30 meters (49 to 98 feet) can achieve speeds of 40 to 80 knots (21 to 41 meters per second). For example, in the case of the USS Ramapo, described in chapter 8, the 342 meter long wave it encountered had a period of 14.8 seconds and a velocity of 23 meters per second. Using equation [11] with Cc = 3 we obtain:

c (meter/sec) = 23                    33                    40

P (Pascal) =                 816,000           1,680,000        2,467,000

P (Pound/sq. ft.) =        17,000             35,100             51,500

In the case of FPSO Schiehallion, (see Appendix 2), bow plates were bent in under wave impacts that were estimated after the fact as:

750,000 to 1,000,000 Pascal locally, and

200,000 Pascal globally.

Later the vessel was instrumented with pressure transducers and returned to station. Peak pressures of 300,000 to 600,000 Pascal due to wave impacts were recorded.[67]

To see what wave pressure is needed to shear hull plates, assume a plate thickness t = 0.0127 meters (0.5 inch) and steel plate with a shearing resistance of s = 689 megapascal (100,000 pounds per square inch) and an opening 5 meters by 5 meters (16.4 feet by 16.4 feet), area A = 25 square meters, with a perimeter p of 20 meters.

The shearing pressure P in Pascal = stp/A                                 [12]

This gives 7,010,000 Pascal or 146,000 pounds per square foot. For these assumptions, it appears that a load concentration factor of Cc = 9 would be required to punch a hole in the hull. As incredible as it may seem, waves can rip steel hulls apart or punch holes in them. This has been amply demonstrated in the case of the Wilstar, the Pittsburgh, and several aircraft carriers.

From Appendix 3

MISCELANEOUS TECHNICAL DATA

Specific gravity (grams per cubic centimeter or metric tons per cubic meter):

Water @ 4 degrees C =1.000

Water at 15 degrees C = 0.99913

Sea water at 15 degrees C =1.025 (average)

Note: sea water depends on NaCl content; 1% =1.0053, 2% = 1.0125, 4% = 1.026, 6% = 1.0413

Ice = 0.917

Mercury at 15 degrees C = 13.559

Crude oil at 60 degrees F = 0.813 to 0.921

Note: crude oil is 6.77 to 7.67 pounds/gallon or 6.8 to 7.8 barrels per metric ton.

Source: Handbook of Chemistry and Physics, 41st ed. 1959, 1923, 2044, 2121, 2130-2131. Cleveland, Ohio: Chemical Rubber Publishing Co.

One standard atmosphere = 76 centimeter (29.92 inches) of mercury = 33.9 feet of water = 1,013 millibars.

Appendix 2: Representative Ship Disasters

(Note: in the interest of conciseness this important Appendix was deleted from the book. It provides the supporting documentation for some of the book’s findings.)

The following list of 70-plus incidents is indicative of the disasters that resulted when ships encounter extreme waves. I have attempted to include incidents where extreme waves damaged a vessel or either caused or contributed to its loss. In some cases there were additional complications, such as fire or explosion. The list spans the time from World War II to the present, and includes various types of vessels large and small, although most are large enough that one would not expect them to have difficulty in rough weather. It is a partial list that only contains a small fraction of the vessels lost at sea during this period. Most, but not all, were lost as a result of the encounter; the few that survived were fortunate to avoid more serious consequences. Some of these incidents are described in greater detail in the body of the chapter, because I wanted to illustrate a particular sea condition. For completeness, their names are listed here also. The bold numbers in parenthesis following the entry refer to the source documents and page numbers that are listed at the end of this appendix.

Oil Tankers and Combination Carriers

As a result of several notorious oil spills (the Amoco Cadiz, in the Atlantic, off the coast of France, the Exxon Valdez, in Alaska, and the Torrey Canyon, near the United Kingdom), much public attention has been focused on the safety of oil tankers. The industry has responded with ever-more stringent safety practices and has taken steps to convert the global fleet from single hull vessels to double hulls. Historically there has been an average of two major spills per year for the years 1960 plus 1965 to 1989. The top 50 spills lost anywhere from 157,000 barrels of crude oil to as much as 1,890,000 barrels. The cause of the disaster is divided almost equally between one of four categories, either (1) collisions, of which there were 11; (2) grounding or stranding, 13; (3) fire/explosion, 12; or (4) structure, hull, or machinery failure, 12. (1, p. 14-17)

Hull and structure failures were primarily caused by weather and heavy seas. So, on the average, about every other year a tanker has been lost, presumably due to weather. Some examples from the National Research Council (1991) reference:

·        Castillo de Bellver (1983) 271,540 dwt. Broke up off of South Africa, followed with fire/explosion. Spilled 239,000 metric tons (1,760,000 barrels) of crude oil. (1, p. 16)

·        T/V Captain W. Arvelo (February 24, 1989) This tanker sank in high winds about 5 nautical miles north of the northeast coast of the Dominican Republic. (7)

·        FPSO Schiehallion (November 19, 1998) 152,360 metric tons. The Schiehallion is a floating production, storage and offloading (FPSO) tanker that is anchored in the North Atlantic Ocean, west of the Shetland Islands. Her length is 245 meters (803 feet), beam is 45 meters (148 feet), and she has a storage capacity of 950,000 barrels of crude oil. On the night of November 19, when the significant wave height was around 14 meters, the vessel was struck on the bow by a high wave. The wave damaged the bow 20 meters (66 feet) above the water line, caving in the bow plating a distance of about 25 centimeters (nearly 10 inches), and causing the vessel to be removed from station and taken to a shipyard for repairs. (2, p. 38)

·        Caribbean Sea (1977) 30,661 dwt. Broke up in east Pacific. (1, p. 16)

·        Athene (1977) 256,000 dwt. This very large crude carrier (VLCC) was sailing in the Agulhas Current off of Port Elizabeth, South Africa, when it encountered an extreme wave. When the wave hit, the foremast was completely submerged and the reinforced windows 17.7 meters (58 feet) above the water line were stove in. It was estimated that the wave was 30 meters (98 feet) high. Faulkner notes that had this been a bulk carrier with a heavy cargo, “she would not have survived.” (3, p. 5-6)

·        Grand Zenith (January 11, 1977) 29,930 dwt. This tanker with 212,000 barrels disappeared in the North Atlantic off of Cape Cod, cause unknown. Bascom states thatwhen this tanker disappeared off of Cape Sable, Nova Scotia, at that time it was the largest ship to be declared “missing, presumed lost.” It carried a crew of 38. (4, p. 151 and 27, p. 273)

·        Golden Drake (1972) 30,000 dwt, Fire/explosion in Atlantic near Bermuda. (1, p. 16, and 5, p. 171)

·        Texaco Oklahoma (March 27, 1971) This tanker with a crew of 44 broke in two while fully loaded at a position about 120 miles northeast of Cape Hatteras, North Carolina. It was proceeding at a slow speed in a severe winter storm (Note: Gulf Stream area!) The forward half submerged the crew sleeping in the forward deckhouse; none of those 13 crew members survived. Hours later a passing ship rescued 13 survivors from the remaining 31 crew members. The coast guard concluded that hull fracture was caused by heavy seas. (25: “Structural Failure and sinking of the Texaco Oklahoma off Cape Hatteras on 27 March 1971, with the loss of 31 lives.”)

·        Pine Ridge (December 21, 1960) Like the Texaco Oklahoma, the Pine Ridge was offshore from Cape Hatteras (about 90 nautical miles, 167 kilometers) but traveling in the opposite direction. Weather worsened and the vessel found itself in a gale. Green water came over the bow and suddenly there was a loud crack and the forward section of the ship tore lose, causing the death of the master, the first, second and third mates, the quartermaster, radio officer and chief steward. The other 29 crew members were rescued and the stern section towed to salvage. The marine board determined that the hull failed due to wastage (corrosion), excessive hogging and sagging stress due to improper ballasting, and heavy seas. Principal members were reduced anywhere from around 20 percent to as much as 65 percent of original design thickness. (25: “MVI Pine Ridge.”)

·        Chryssi (December 26, 1970) 29,653 dwt. This 190 meter (624 feet) long tanker broke up in the Atlantic Ocean near Bermuda. It was carrying 226,000 barrels of oil. (5, p. 171)

·        Paco Ocean (1969) 30,016 dwt. Broke in two, Northwest Pacific. (1, p. 16)

·        Keo (1969) Hull failure off of Massachusetts. (1, p. 16)

·        World Glory (June 14, 1968) Only 10 of 34 crew survived; 334,000 barrels of crude oil went into the Indian Ocean. See Chapter 9. (7)

Others:

• Prestige (November 13, 2002) This tanker was hit by high waves off of Galicia coast, Spain. It developed a hole in its side, started leaking, was towed to deep water, broke in two, and sank, releasing 77,000 tons of oil (approximately 448,000 barrels). (6)
• Erika (December 12, 1999) This tanker broke in two in heavy seas, gale force winds near Brest, France. Corrosion suspected as part of the problem, 71,400 barrels of oil spilled. (8, p. 1)
• Nakhoda (January 7, 1997) This Russian tanker carrying 36,400 barrels of oil broke in 2 pieces in heavy seas northwest of Japan. (28)
• Mimosa (August 1991) This 357,000 dwt tanker had her rudder badly damaged during a storm. The vessel then drifted helplessly in the Agulhas Current, in relatively shallow waters that were from 55 fathoms to 110 fathoms (100 to 200 meters) deep. She came dangerously close to going aground in Algoa Bay, South Africa, but disaster was avoided by a marine salvage company. Another report stated that a large wave punched a hole in the side plating of the hull, large enough to “drive a bus through.” (11, p. 28, and 12, p. 4)
• Atigun Pass (1982 or 1983) See Chapter 9.
• Cretan Star (July 28, 1976) This tanker had a load of 28,600 tons of crude oil. After leaving the Persian Gulf she encountered a storm. The master radioed that she’d been hit by a huge wave that caused some damage and oil leakage. That was the last word from the vessel. A subsequent search by aircraft found an oil slick not far from Bombay, India, near the ship’s last reported position. (4, p. 61)
• Wilstar (May 17, 1974) 132,000 dwt. It fell into a huge trough off South Africa, then was hit by a rogue wave in the Agulhas Current. The vessel was heavily damaged, with a large section of the bow, fabricated of 2.54 centimeter (1 inch) thick steel plates, literally ripped away as if grabbed by a giant hand. (10, p. 16 and 4, p. 64)
• Wafra (February 27, 1971) 70,000 dwt. A tanker damaged by an extreme wave in the Agulhas Current. Engine room flooded, taken under tow, towline broke, and the vessel drifted onto the Agulhas Reef. (7 and 4, p. 64)
• World Horizon (1973?) Supertanker damaged by an extreme wave in the Agulhas Current. (4, p. 64)
• Bridgewater (January 30, 1962). This tanker broke in two in a storm 230 nautical miles northwest of Fremantle, Australia. The stern half was eventually towed in for salvage. (27, p. 28)
• Marine Sulphur Queen (February 4, 1963). The Marine Sulphur Queen (169 meters, 554 feet) was a somewhat unusual tanker.  It had been converted to carry molten sulfur. The last known contact with the vessel occurred when her position was estimated as 25 degrees, 45 minutes north, 86 degrees west. This would have placed her in the gulf of Mexico around 250 nautical miles (463 kilometers) due south of Panama City, Florida. The vessel and crew disappeared without a Mayday or trace. After several weeks of searching, a life preserver, fog horn, and trail board with the vessel’s name were found. Weather was known to be rough along the vessel’s route, winds 25 to 46 knots, seas at around 5 meters (16 feet.) Originally, it was thought that the vessel might have been sunk by a rogue wave. However, the coast guard inquiry revealed that the vessel had a history of fires in the insulation surrounding the molten sulfur tanks and had experienced damage in two previous storms. The Board of Inquiry concluded that the vessel might have exploded, may have broken in two due to a failure of the hull girder, or may have capsized in synchronous rolling. (25, report 5943 and  27, p. 125)

General Cargo, Bulk Carriers and Combination Carriers (OBOs)

Bulk carriers are the one vessel type that appears to be most susceptible to break-up by large waves. An appalling number of bulk carriers have been lost in the last several decades, along with hundreds of crew.

• Fei Cui Hai (February 7, 1998) The China Overseas Shipping Company bulk carrier was lost in the South China Sea between southern Vietnam and Singapore with 31 of the crew of 34 dead. (18)
• Flare (January 16, 1998) This bulk carrier broke up and sank in the Gulf of St. Lawrence; 4 crew were rescued by a Canadian helicopter but 21 were lost. (18)
• Viking (September 16, 1994) Viking, a collier, was hit by huge waves off the coast of Norway, suffering 21 injured crew.
• Berge Istra (December 1975) This 224,000 ton combination bulk carrier is the biggest ship ever to simply disappear without a trace. It was 314 meters (1,030 feet) long, with a beam of 50 meters (164 feet). Lost after sailing from Tubarão, Brazil on Nov. 29, 1975. Last reported southwest of Mindanao, Philippines. For weeks no one knew what happened to the ship. Originally, because of its sudden disappearance, it was thought to be the victim of an extreme wave. Later, two survivors were rescued. They reported that the ship had exploded without warning, broke up, and sank before a Mayday call could be made. (13, p. 198 and  4 p. 153)
• Anita (March 1973) 13,000 dwt. This Norwegian bulk carrier sailed from Virginia with Germany as its destination. In the North Atlantic it reported encountering a severe gale—60 knot winds, 15 meter (49 foot) seas; nothing was ever heard from the ship again. It thus became one of the hundreds of vessels to be entered on Lloyd’s List as “missing, presumed lost.” (4, p. 158 and 14, p. 19)
• Norse Variant (March 1973) In the North Atlantic with a cargo of coal, this 165 meter (542 foot) long vessel broke in two during the same storm as the Anita and sank at a position about 114 nautical miles southeast of Cape May, New Jersey. Waves broke a hatch cover and the ship sank quickly. In this case, a single survivor was rescued and thus the story of the ship’s disappearance became known. This vessel also served as a car transporter for Volkswagen automobiles. (4, p. 158 and 14, p. 19)
• M/V Sinar Andelas (December 26, 2004) This cement carrier was in the port of Lhok Na, Indonesia, when the wave from the December 26, 2004 southeast Asia tsunami hit. The vessel capsized; of  23 members, 19 were reported missing. (18)
• Theodore AS (1973) 13,900 dwt. This bulk carrier sailed from Norway headed for Spain with a cargo of iron ore. She was struck by a gale in the North Sea and disappeared, becoming another entry on Lloyd’s List of “missing, presumed lost.” (4, p. 159)
• Neptune Sapphire (1973) See Chapter 8.
• Atlas Pride (Date unknown) This was another cargo ship hit in terrible weather. A rogue wave appeared out of nowhere and destroyed the entire bow. (12 , p. 4)
• Apollo Sea (June 20, 1994) A bulk ore carrier lost at the Cape of Good Hope after foundering in heavy weather—36 crew lost, damage to endangered African Penguin breeding grounds from oil spill. (9, p. 1)
• MV Treasure (June 23, 2000) Another bulk ore carrier foundered near same location as Apollo Sea—this time in fair weather, with the loss of 1,400 metric tons of oil. (9, p. 1)
• Edmund Fitzgerald (November 19, 1975) See Chapter 9.
• Selendang Ayu (December 10, 2004) This 226 meter (740 feet) long Malaysian freighter with a cargo of soybeans lost power when hit by big waves in the Bering Sea. Gale force winds continued to blow it toward Unalaska Island, despite efforts to tow it or anchor it. The vessel went aground on the island and broke in half, releasing 154,000 liters (40,000 gallons) of fuel oil. Six evacuated crew members died in a helicopter crash. (15, p. 1)
• Unnamed vessel (1960s) This bulk carrier was carrying ore from North Africa to England. Off the northwest coast of Spain, along the 100 fathom (183 meters deep) line, the ship was making good progress in moderate weather. At 0520 hours (5:20 A.M.), the chief officer was surprised to see the moon blotted out and the deck of the ship obscured. At first, he thought a cloud had passed over the moon, but then to his horror realized that a giant wave was bearing down on the port beam of the vessel. Just before reaching the ship, the wave started to break, hitting it and sweeping the full length of the vessel. Fortunately the hatch covers did not fail and the ship survived, although with damage that indicated the enormous force of the blow it received. The forecastle head deck was bashed in about 7.6 centimeters (3 inches), with supporting deck beams (35.6 centimeter or 14 inch wide steel channel beams) being cracked through; 12.7 centimeter (5 inch) stanchions were buckled; timber supports and shelving below decks completely wrecked; flood lights and ladders 15.3 meters (50 feet) above the sea ripped loose; glass on compasses 21.4 meters (70 feet) above the water line were cracked, even though they were protected by brass helmets. Finally, it was determined from other damage that the wave was higher than 26 meters (85 feet). Ironically the chief officer had warned the master of the risk of extreme waves in shallow waters along the Spanish coast, but the master elected to stay on the course he’d laid out. (16, p. 35-37)
• Daniel J. Morrell (November 29, 1966) This 183 meter (600 foot) long ore carrier embarked to pick up another load of iron ore. Unfortunately it was caught in a violent late fall storm on Lake Huron. The ship broke in two, stranding some crew members in the bow section. The stern section drifted away. Four men got a raft launched and abandoned the bow section which sank first. After a day and a half when rescuers located the raft in freezing weather, only one person remained alive. (17, p. 41)
• Carl D. Bradley (November 18, 1958) See Chapter 9.

·              SS Pennsylvania ( January 9, 1952) The SS Pennsylvania departed Seattle for Yokohama, Japan. The vessel was loaded with a cargo of wheat and barley and additional army supplies, including army trailers and dump trucks. Some cargo was stored on deck. En route the vessel encountered gale-force winds and seas of 11 to 14 meters (35 to 45 feet). Early on the morning of January 9, the vessel reported that there was a 4.3 meter (14 foot) long fracture in the hull and the vessel was coming about to return to Seattle. At that time she was at 51 degrees, 9 minutes north, 141 degrees 31 minutes west, in the North Pacific southwest of Queen Charlotte Islands. Problems developed with the steering gear, and the vessel lost steering. The vessel was taking on water forward and in the engine room. The gear was repaired but then the vessel reported that she was having difficulty steering because the rudder was too far out of the water. The last message received was around 10 P.M. advising that the crew was abandoning ship. Despite a search, nothing was ever found of the vessel or its 46 crew members. (25: “MVI Pennsylvania”)

Container Ships

Container ships have been hit by extreme waves, with the result that some containers were damaged or lost over board, as in the case of the Hansa Carrier described in Chapter 2. Instances where a container ship has been broken up or capsized by extreme waves are uncommon. I met with two masters of container ships, Captain Jon Harrison and Captain Mark Remijan, and asked them if they had ever experienced a rogue wave. Jon said that he had not experienced anything he considered an extreme wave, just storm waves 12 to 15 meters (39 to 49 feet) high. Mark said that he thought he might have experienced one. This was on the President Jackson. See below for a description of that incident.

·        M/V Xin Qing Dao (October 27, 2004) This brand new (built in 2003) 5,600 TEU container ship is 279.9 meters (918 feet) long, has a beam of  40.3 meters (132 feet) and a draft of 14 meters (46 feet). En route from Malta to Hamburg, she encountered a Beaufort Force 11 storm off the coast of Brittany. Waves reached 30 meters (98 feet) and the vessel experienced rolling of 30 degrees. A total of 31  12.2 meter (40 foot) long containers were lost overboard and 29 more were damaged. The vessel was able to reach the port of Felixstowe, United Kingdom, on October 30, 2004. (18)

·  M/V OOCL America (January 31, 2000) En route from Long Beach to Kaohsiung, this vessel encountered a severe North Pacific storm. A wave caused the vessel to roll 45 degrees, causing an estimated 350 containers to be lost overboard and several more to be crushed. There was also flooding and damage to container bays, but the vessel did not sink. Two other container ships were damaged in the same storm: M/V Sea-Land Hawaii (lost 21 containers) and M/V Sea-Land Pacific (lost 20 containers). (18)

·  M/V Jaami (December 26, 2004) This container ship was entering Colombo as the southeast tsunami of December 26, 2004 hit. The vessel was driven against the breakwater where it was abandoned but later salvaged. (18)

·   M/V MSC Carla (November 25, 1997) This 40,912 dwt container ship was en route from LeHavre, France to Boston carrying 2,400 containers when it encountered a gale and seas of  9.2 meters (30 feet) or greater.  Early on the morning of November 25, about 100 nautical miles north of São Miguel Island, Portuguese Azores, the ship broke in two pieces. Portuguese military helicopters rescued 34 crew members. The bow section sank on November 30, with about half of the containers. The stern section, with another 1,000 containers, was towed to Las Palmas, Canary Islands, for salvage. (18)

• Hanjin Inchon (1997-1998) Container ship reportedly lost with all hands. No details available.
• Poet (October 25, 1980) Poet was a converted Liberty Ship, originally launched in 1944. It was carrying a cargo of grain to Egypt when it vanished during a storm, leaving no trace. The Marine Inquiry Board listed a number of possible reasons why the ship might have been lost, including hatch failure, structural failure, or capsizing, but was unable to reach any definite conclusion. The crew of 34 was lost.  (25 and 27, p. 164-165)
• Badger State (December 26, 1969) This vessel, like Poet, was a 135 meter (441 foot) long cargo vessel built in 1944. It suffered an unusual disaster. The vessel was loaded with bombs and ammunition destined for Vietnam. It encountered two successive storms in the North Pacific. One mountainous wave rolled the vessel 52 degrees, destroyed one lifeboat, and under the force of violent rolling, some of the cargo broke loose. An explosion opened a hole in the side of the ship. The crew of 40 sent a Mayday and prepared to abandon ship. While lowering a lifeboat, a 2,000 pound bomb fell out of the hole and landed in the lifeboat, capsizing it. There were 14 survivors. (25: “SS Badger State”)
• President Jackson (1992) This was a C-10 class vessel, 1st generation Post-Panamax, capacity around 4,300 TEUs, launched in 1988. The master told me that  they were in the Bering Sea, had been in a storm for about 6 hours with 7 to 8 meter high swells in a quartering sea. The vessel was rolling 15 to 18 degrees, occasionally 20 degrees. It was daylight; he happened to look aft and saw a wave, much larger than the others, coming towards the stern quarter. When it hit, the President Jackson rolled 32-33 degrees. As the wave passed under the ship, it seemed to just hang there in space, you could feel a strong vibration or shudder run through the ship. The master threw the rudder over 20 degrees to counteract the roll. He was not sure of the height of the wave, it all happened too fast, but stated that it was significantly different from the 7-8 meter waves the ship had been experiencing. It only happened once. (19)
• Hansa Carrier (May 27, 1990)  See Chapter 2. While in the center of the North Pacific, roughly midway between the Aleutian and Hawaiian Islands, the vessel encountered a severe storm. Waves hitting the vessel caused 21 containers to fall into the sea, spilling their contents of athletic shoes.

Passenger Liners/Cruise Ships

There have been a number of instances where passenger liners caught fire and burned up. Most striking of these was the Yarmouth Castle (Caribbean Sea, November 13, 1965), where the captain was the first to leave, and was locked up on one of the rescue vessels for failing to help save the passengers. Others include such well-known vessels as Leonardo da Vinci, Cunard Ambassado, Homeric, Caribia, Laconia, Morro Castle, and Antilles. (27)  Passenger liners have not been immune to damage by extreme waves, as these examples indicate:

• Norwegian Dawn (April 16, 2005) The “Ocean view” staterooms on the port and starboard sides of the luxury cruise ship Norwegian Dawn command an excellent view of the sea from the 10th deck. There is a large bed, private bathroom, clothes closet, sitting area with couch, small table, and a desk with a television. Floor to ceiling glass doors open to a private balcony. The 294 meter (965 feet) long vessel sailed from New York on Sunday, April 10, 2005, for a visit to Florida and the Bahamas, and was due to return to New York on Sunday, April 17, 2005, to load passengers for the next cruise. Upon leaving the Bahamas for New York, the Norwegian Dawn ran into a gale. Seas and winds coming down from the north were running in opposition to the northbound Gulf Stream. Weather was rough for the next 48 hours after the Norwegian Dawn left the Bahamas, with the vessel rolling in 12 meter (40 feet) high swells. Early Saturday morning the vessel was hit by a single freak wave 21.4 meters (70 feet) high that caved in the sliding glass doors in several forward-facing cabins. A flood of sea water rushed into the Norwegian Dawn, flooding 62 cabins. Passengers reported broken glass, clothing, newspapers, magazines floating in sea water, furniture overturned. Four passengers received minor injuries. The Norwegian Dawn diverted to Charleston South Carolina for emergency repairs and to allow passengers whose cabins had been flooded to fly back to New York. In Charleston, the U.S. Coast Guard reported that the vessel had experienced some hull damage but was not taking on any water. (20)
• M/V Explorer (January 27 2004) See Chapter 9.
• Monique (August 1, 1953). This French passenger ship vanished in the South Pacific with 120 persons on board. (27, p. 271)
• Caledonian Star (March 2, 2001) See Chapter 9.
• M/V Rotterdam (September 24, 2004) This 237 meters (777 feet) long, 62,000 ton Holland America cruise ship found itself on the edge of hurricane Karl. Battered by waves in rough seas it lost all power to 4 engines, disabling the stabilizers and allowing the vessel to list as much as 40 degrees in 10 to 15 meter (33 to 49 foot) swells. Passengers suffered numerous minor injuries and fractures and reported furniture flying around, pianos rolling, plates crashing to the floor, TV sets rocketing across staterooms. (18)
• Bremen (February 22, 2001) See Chapter 9.
• Oceanos (August 3,1991) During a storm off of East London, South Africa, the cruise ship Oceanos (150 meters, 492 feet long) was battered by severe wind and wave conditions and hit by an extreme wave or waves. There was a leak in the engine room, power failed and the vessel sank. All passengers and crew (580 persons) were rescued. This was the same storm that damaged the Mimosa. (11, p. 28)
• Queen Elizabeth 2 (September 11, 1995) See Chapter 9.
• Michelangelo (April 12, 1966) See Chapter 9.
• Queen Elizabeth (1943) See Chapter 9.
• Queen Mary (1942) See Chapter 9.
• Waratah (July 27, 1909) See Chapter 9.

Other types of Vessels

• Polar Star (October 25 1985) The U.S. Coast Guard icebreaker Polar Star was the first single ship to circumnavigate the North American continent by traversing the Northwest Passage. After successfully completing the dangerous passage through ice-filled waters, the 122 meters (399 feet) long vessel was not far from Vancouver Island and was traveling south east to Seattle when it was hit on the starboard beam by a sequence of extreme waves—the so-called “Three Sisters.” This was thought to be due to the interaction of increasingly heavy seas the vessel was headed into, combined with a storm that had been building to the west of the vessel for over 36 hours across a fetch of 1,613 kilometers (1,000 miles). The waves came suddenly out of the darkness at 0200 (2:00 A.M.), causing the vessel to roll violently back and forth 50 degrees. Three crew were tossed the width of the 26 meter (85 feet) wide bridge, killing one and injuring two others. Winds reached 60 knots with gusts to 80. The significant wave height was around 3.5 meters (11.5 feet), while the “Three Sister Waves” that struck the ship were estimated as three times as high, or 10.7 meters (35 feet). (21, p. 190-196)
• Nepenthe (1983) See Chapter 9.
• Leviathan (June 8, 2001) Leviathan, a 9.8 meter (32 foot) Down East cutter was less fortunate than Nepenthe. With a 2-person crew, the vessel left the Chagos Archipelago (near Diego Garcia Island) headed for Ile de Mayotte, a small island in the Comoros, in the dangerous waters of the Mozambique Channel. On the evening of June 8, they reported experiencing high winds and heavy seas. That was the last that was heard from them until their EPIRB was detected about 6 hours later at latitude 10.17 degrees south, longitude 49.67 degrees east. At this time of year, the South Equatorial Current branches to flow around Madagascar, joining up again at the southern end of the island to form the Agulhas current. They would have passed through this turbulent area, and were likely overwhelmed by confused seas. (26, p. 64-65)
• Trawler Gaul (1974) This modern, 1,500 ton “super” trawler went down in a storm with 36 crew and was never heard from. Rumors flew about that it had been torpedoed by a Soviet submarine, pulled under by a nuclear submarine, or sunk by a rogue wave. The wreck was finally located in 1997, surveyed a few years later, and at an official hearing in 2004, it was determined that the vessel capsized due to flooding through open duff and offal chutes on the factory deck. (24)
• Lady Alice (September 6, 1980) See Chapter 9.
• U.S.S. Grouper See Chapter 9.
• The U.S.S. Valley Forge, an aircraft carrier, was hit by an extreme wave during a strong winter storm near Cape Hatteras in the Gulf Stream. The wave was more than twice the significant wave height and crashed down on the starboard side of the forward flight deck so hard that it ripped the deck from the ship. Steel girders and the 15.2 centimeter (6 inch thick) teak flight deck were broken off and lost overboard. Photographs show sections of the junior officer’s quarters dangling off the side of the ship; fortunately, the area was unoccupied at the time of the incident. (22; 10, p. 17)
• Műnchen (December 1978) This state-of-the-art German cargo ship sent a frantic Mayday radio call from the middle of the Atlantic. Despite a massive search effort by dozens of ships in the vicinity, neither the vessel nor survivors were ever found. Searchers did find one of the vessel’s lifeboats, normally stowed at a location 20 meters (66 feet) above the water line. Damage to the lifeboat supports indicated that it had been ripped off the boat by the force of a large wave. Twenty-seven crew were lost. (12)
• The U.S.S. Independence (April 7-8, 1977) This was another aircraft carrier that was hit by several extreme waves during a North Atlantic Storm. The captain was quoted as saying that he looked out and saw the wave coming a mile or mile and a half away (1.6 to 2.4 kilometers), and it looked like the wave in the “Poseidon Adventure” (a movie depicting a passenger ship being capsized by a huge wave at sea). The significant wave height at the time was 7.6 to 9.2 meters (25 to 30 feet); the wave that struck the carrier was around 16.7 to 18.3 meters (55 to 60 feet). (23, p. 14)
• U.S.S. Milwaukee (October 1975) See Chapter 9.
• Ob (circa 1955-56) This Soviet diesel/electric Antarctica supply ship, reported being hit by a 25 meter (82 feet) wave in the Southern Ocean. (4)
• U.S.S. Pittsburgh (February 1945) See Chapter 9.

_________________________

Sources for the above incidents:

1.      Committee on Tank Vessel Design. 1991. Tanker Spills—Prevention by Design. National Research Council, National Academy of Sciences, Washington DC: National Academy Press, 14-17.

2.      Gorf, Peter, et al. 2001. “FPSO Bow Damage in Steep Waves.” In Olagnon and Athanassoulis, eds., 37-46.

3.      Faulkner, Douglas. 2001. “Rogue Waves—Defining their Characteristics for Marine Design.” In Olagnon and Athanassoulis, eds., 5-6.

4.      Bascom, Willard. 1980. Waves and Beaches. New York: Anchor Press.

5.      Couper, Alistair, ed. 1983. The Times Atlas of the Oceans. New York: Van Nostrand Rheinhold.

6.      www.CNN.com.world . 2002.  “Crippled Fuel Oil Tanker Sinks,” Wednesday, November 20.

7.      National Oceanic and Atmospheric Administration (NOAA). “Oil spill incident reports.” http://spills.incidentnews.gov. Accessed September 2005.

8.      International Oil Pollution Compensation Funds “The Erika Incident.” http://www.iopcfund.org/erika.htm. Accessed September 2005.

9.      International Bird Rescue Research Center. “IBRRCs Big Assist at Oil Spill in South Africa,” http://www.ibrrc.org/treasure_spill.html. Accessed September 2005.

10.  Nickerson, Jerome W. 1993. “Freak Waves.” Mariners Weather Log, Vol. 37, No. 4.

11.  Shillington F.A. and E. H. Schumann. 1993. “High Waves in the Agulhas Current.” Mariners Weather Log, Vol. 37, No. 4.

12.  B British Broadcasting Corporation. 2002. “Rogue Waves.” Transcript of a BBC program on Freak Waves. First aired on BBC TWO, November 14, 2002.

13.  Hendrickson, Robert. 1984. The Ocean Almanac. New York: Doubleday

14.  Kjeldsen, Soren Peter. 2001. “Measurements of Freak Waves in Norway and Related Ship Accidents.” In Olagnon and Athanassoulis, eds., 19-35.

15.  Milbury, Jim. 2005. “Bering Sea Shipwreck Spill Threatens Alaskan Islands,” NOAA Report, Vol. XIV, No.1, 1.

16.  Cameron, Captain T. Wilson. 1993. “The Treachery of Freak Waves” Mariners Weather Log, Vol. 37, No. 4, 35-37.

17.  Gillham, Skip. 1993. “The Daniel J. Morrell.” Mariners Weather Log, Vol. 37, No. 4, 41.

18.  The law firm of Countryman and McDaniel. “Marine Casualty Reports.” See Http://www.cargolaw.com/presentation-casualties. Used with permission.

19.  Personal communication, Captain Mark Remijan, June 5, 2005.

20.  “Cruise Ship Damaged, Flooded by 70-foot Wave During Storm.” Washington Post, April 18, 2005, p. A18. Also articles posted on www.CNN.com/2005/TRAVEL on April 17 and April 19, 2005, and Abbott, Mary Lu, “Rogue Waves Surprisingly Common,” Los Angeles Times, May 22, 2005, pg. L-5. In June, a group of passengers filed a \$100 million lawsuit, claiming the cruise line had needlessly endangered their lives. See Los Angeles Times, June 26, 2005, p. L3. Passengers allege that despite knowing about the storm, the vessel attempted to return to New York to take part in a television show.

21.  Nickerson, Jerome W. 1986. “Three Sisters Mar Historic Voyage.” Mariners Weather Log, Vol. 30, No. 4, 190-196.

22.  Personal communication, Admiral Joe Barth, April 20, 2005.

23.  Nickerson, Jerome W.  1985. “Marine Observations Program,” Mariners Weather Log, Vol. 29, No. 1, 14.

24.  “Inquiry Into the Loss of the “Gaul.” 2002.  Mr. Justice David Steele presiding, December 17, London: UK Department of Transport.

25.  Marine Board of Investigation Reports (Marine Casualty Report), United States Coast Guard, U.S. Department of Transportation. See http://www.uscg.mil/hq/g-m/moa/reportindexcas.htm. Accessed June 2005.

26.  Griffiths, Jenni. 2002. “Without a Trace.” Cruising World, December, 64-81.

27.  Ritchie, David. 1996. Shipwrecks—An Encyclopedia of the World’s Worst Disasters at Sea. New York: Checkmark Books.

28.  See the Cargo Letter, Edition 310, January 6, 1997 at http://www.interpool.com/cargoletter. See also the National Maritime Research Institute (Japan) for a photograph of the bow section just before sinking. http://www.nmri.go.jp.

Annotated Bibliography
(This is the complete list of references and source material for the book.)

Aebi , Tania (with Bernadette Brennan). 1989. Maiden Voyage. New York: Ballantine Books. Aebi left New York at age 18, returning two and one-half years later as the youngest woman to sail around the world alone.

Ambraseys, N. N. 1962. “Data for the Investigation of the Seismic Sea Waves in the Eastern Mediterranean.” Bulletin of the Seismological Society of America, 895–913. Includes a description of the modified Sieberg Tsunami Intensity Scale.

Antar, Elias. 1971. “Earthquake!” Saudi Aramco World, May/June, Vol. 22, No. 3. Descriptions of some ancient earthquakes in the Middle East.

Barker, Ernie. 1998. Rogue Wave. Unpublished manuscript. A single-handed sailor’s journal of wave adventures in the Tasman Sea.

Barr, Edward J. 1994. “Freak Wave on a Submarine.” Mariners Weather Log, Vol. 38, No. 4. Report describing a large wave overrunning a submarine as it was in the process of diving to periscope depth and the consequences.

Bascom, Willard. 1980. Waves and Beaches. New York: Anchor Press. A classic book, very well written by the man responsible for the Mohole Project.

Battjes, J. A., ed. 1985. Behaviour of Offshore Structures—Proceedings of the 4th International Conference on Behaviour of Offshore Structures (BOSS ’85). Amsterdam: Elsevier. A compendium of papers on offshore structure design criteria and methods.

Beach, Edmund E. 1966. The Wreck of the Memphis. New York: Holt, Reinhart and Winston. Story of an armored cruiser driven aground in a shallow harbor by large waves.

Belenky, Vadim. 2004. “Demystifying Parametric Roll.” Surveyor, fall, 26–29. Report on the causes of parametric rolling and how to avoid it.

Bergreen, Laurence. 2004. Over the Edge of the World. New York: Perennial. The story of Magellan’s historic circumnavigation.

Bernard, Eddie, et al. (Hokkaido Tsunami Survey Group). 1993. Tsunami Devastates Japanese Coastal Region. Seattle: Pacific Marine Environmental Laboratory, NOAA.

Available http.//www.pmel.noaa.gov/tsunami/okushiri­_devastation.html. Accessed 8/24/05. A description of the Hokkaido tsunami and the performance of tsunami walls.

Bitner-Gregersen, Elzbieta. 2002. “Extreme Wave Crest and Sea State Duration.” Appendix B4. In A. D. Jenkins, et al. Research Report No. 138. Bergen: Norwegian Meteorological Institute, August 27. An analysis of extreme waves with a discussion of the Draupner wave of January 1, 1995.

Borrero, Jose, et al. 2005. “Could It Happen Here?” Civil Engineering, April, 54–65, 133. An investigation into the likelihood and consequences of a tsunami in Southern California.

Bowditch, Nathaniel. 2000. The American Practical Navigator—An Epitome of Navigation, 2002 Bicentennial Edition. Bethesda, Maryland: U.S. Government National Imagery and Mapping Agency. The classic “bible” of sailors and mariners.

British Broadcasting Corporation. 2002. “Rogue Waves.” Transcript of a BBC program on freak waves. First aired on BBC TWO, November 14, 2002. An interesting narrative by people interviewed, including the captain of Queen Elizabeth 2.

Bryant, Edward. 2001. Tsunami—The Underrated Hazard. Cambridge: Cambridge University Press. Bryant is the first author to raise the question of a much greater tsunami risk in a documented, thorough manner. The best book on tsunami there is. His book is now prophetic.

Burgess, Robert F. 1970. Sinkings, Salvages and Shipwrecks.  New York: American Heritage Press. The story of salvage efforts at Port Royal, Jamaica.

Butler, Hal. 1974.  Abandon Ship. Chicago: Henry Regnery Company. Accounts of the sinking of the Carl Bradley, the Edmund E. Fitzgerald and the Flying Enterprise.

California State Lands Commission. 2005. “Marine Oil Terminal Engineering and Maintenance Standards (MOTEMS).” California Code of Regulations, Chapter 31F of Div. 1-11, Title 24, Part 2, Vol. 1, January 19. A new, very comprehensive design standard for harbor structures.

Carr, Michael W. 1999. Weather Predicting Simplified. New York: International Marine. An excellent handbook on weather for the sailor or mariner.

Carracedo, J.C. 1994. “The Canary Islands: An Example of Structural Control on the Growth of Large Oceanic-Island Volcanoes.” Journal of Volcanology and Geothermal Research, Vol. 60, 225–241. Describes the volcanoes in the Canary Islands.

Carrier, Jim. 2001. The Ship and the Storm—Hurricane Mitch and the Loss of the Fantome. New York: International Marine/McGraw-Hill. Hurricane (Mitch) that seemed to stalk a modern tall ship, the Fantome.

Chapman, Charles F. 1976. Piloting, Seamanship and Small Boat Handling. 52nd ed. New York: The Hearst Corporation, Motor Boating and Sailing Division. The bible of all sailors and boat captains.

Chen, Henry, Vincent Cardone and Peter Lacey. 1998. “Use of Operation Support Information Technology to Increase Ship Safety and Efficiency,” SNAME Transactions, Vol. 106, 105–127. An excellent overview of technology for optimal routing of merchant ships taking into account forecasted weather and the dynamic parameters of the vessel.

Chryssostomidis, Chryssotomos and Jerome J. Connor, eds. 1983. Behaviour of Off-Shore Structures, Proceedings of the Third International Conference. Vol. 1. New York: Hemisphere, 18-49. A compendium of papers on offshore structure response to static and dynamic structural loads.

Coffman, Jerry L. and Carl A. von Hake, eds. 1973. Earthquake History of the United States, Publication 41-1. Rev. ed. Washington D.C.: U.S. Department of Commerce, National Oceanic and Atmospheric Administration. Material facts about tsunami and the earthquakes that caused them.

Coles, K. Adlard (revised by Peter Bruce). 1996. Heavy Weather Sailing. Camden, Maine: International Marine. A classic book about yacht handling in gales.

Committee on Tank Vessel Design. 1991. Tanker Spills—Prevention by Design. National Research Council, National Academy of Sciences, Washington DC: National Academy Press. A summary report on oil tanker spills and ways to improve vessel design and reliability following the Exxon Valdez disaster.

Couper, Alistair, ed. 1983. The Times Atlas of the Oceans. New York: Van Nostrand Rheinhold.

Cummins, John. 1978. The Voyage of Christopher Columbus—Columbus’ Own Journal of Discovery Newly Restored and Translated. New York: St. Martins Press. An annotated version of Columbus’ log from his first trip to America.

Donaldson, Sven. 1999. “Scenes from Hell—The Sydney–Hobart Race Turns Tragic.” Ocean Navigator, No. 96, 56–63, March/April. Summary report on the 1998 Sydney-Hobart race.

Dor-Ner, Zvi. 1991. Columbus and the Age of Discovery. New York: William Morrow and Company. An excellent illustrated book describing Columbus and his voyages of exploration and discovery.

Dudley, Walter C. and Min Lee. 1998. Tsunami! 2nd ed. A Latitude 20 Book. Honolulu: University of Hawai’i Press. History of tsunamis with emphasis on the Pacific region, Alaska, and Hawaii. Description of tsunami warning systems and the Pacific Tsunami Warning Center.

Dyson, John. 1991. Columbus for Gold, God and Glory. New York: Simon & Schuster. History of Columbus and his discovery of the new world.

Dysthe, Kristian B. 2000. “Modeling a Rogue Wave—Speculation or a Realistic Possibility.” In Olagnon, M. and G.A. Athanassoulis, eds. 2001. Rogue Waves 2000, 255-264. A description of some of the characteristics of rogue waves and various theories being advanced to model them.

Ebbesmeyer, Curtis C. and W. James Ingraham, Jr. 1992. “Shoe Spill in the North Pacific.” Eos, Vol. 73, No. 34, August 25, 361-368. A classic study of current movements based on shoes discharged into the ocean when containers spilled from a ship during a storm.

Edge, Billy E., ed. 2001. Ocean Wave Measurements and Analysis. Vol.1. Proceedings of the 4th International Symposium Waves. Reston, Virginia: American Society of Civil Engineers. Review of wave measurement and analysis techniques.

European Space Agency. 2004. The MaxWave Project. www.esa.int/esaCP/SEMOKQL26WD_index_0.html.  Accessed 9/2/2004. Scope of work and various reports on this pioneering study of rogue waves.

Farrington, Tony. 1996. Rescue in the Pacific—A True Story of Disaster and Survival in a Force 12 Storm. Camden, Maine: International Marine. The story of a weather bomb and its unexpected impact on a sailing regatta from New Zealand to the island of Tonga.

Faulkner, Douglas, et al., eds. 1984. The Role of Design, Inspection, and Redundancy in Marine Structural Reliability. Proceedings of an International Symposium, November 14–16, 1983. Committee on Marine Structures, National Research Council, Washington DC:  National Academy Press. Design of ships and offshore structures from the viewpoint of safety and reliability.

Finney, Ben. 1994. Voyage of Rediscovery—A Cultural Odyssey through Polynesia. Berkeley: University of California Press. Thorough treatment of ancient Polynesian sailing and navigation techniques, along with a description of the Hokule’a’s various trips.

Flayhart, William Henry III. 2003. Perils of the Atlantic—Steamship Disasters 1850 to Present. New York: W. W. Norton. Story of the SS Pennsylvania and other steamship disasters.

France, William N., et al. 2003. “An Investigation of Head-Sea Parametric Rolling and Its Influence on Container Lashing Systems.” Marine Technology, Vol. 40, No. 1, January, 1-19. A study of the dynamic forces and mechanisms involved in parametric rolling.

Frazier, Kendrick. 1979. The Violent Face of Nature—Severe Phenomena and Natural Disasters. New York: William Morrow. Discusses storms, earthquakes, flooding and so on, along with forecasting and warning systems, disaster preparation and response.

Frump, Robert. 2001. Until the Sea Shall Free Them—Life, Death and Survival in the Merchant Marine. New York: Doubleday. Detailed account of the Marine Electric disaster.

Goss, Michael and George Behe. 1994. Lost At Sea—Ghost Ships and Other Mysteries. Amherst, New York: Prometheus Books. Discussion of the SS Waratah incident.

Gower, Jim. 2005. “Jason 1 Detects the 26 December 2004 Tsunami.” EOS Transactions AGU, Vol. 86, No. 4, 37. Available http//www.agu.org/pubs/crosssref/2005/2005EO040002.shtml. Accessed 10/2/05. Report concerning the Jason 1 satellite observations of a tsunami wave passage in the Indian Ocean.

Gunson, Jim, Susanne Lehner and Elzbieta Bitner-Gregersen. November 2001. “Extreme Wave Conditions from Wave Model Hindcasts and from Synthetic Aperture Radar Image.” In Design and Operation for Abnormal Conditions II. London: Proceedings Royal Institute of Naval Architects.  New evidence for extreme waves.

Heideloff, Christel and Richard Monden. 2005. “ISL Market Analysis 2005: World Merchant Fleet, OECD Shipping and Shipbuilding.” In Shipping Statistics and Market Review, January/February. The Institute of Shipping Economics and Logistics, (ISL).  www.isl.org p.1-2.  Accessed 3/25/05. An excellent source for merchant shipping statistics and data.

Hendrickson, Robert. 1984. The Ocean Almanac. New York: Doubleday. A compendium of miscellaneous facts about ships and the oceans.

Herdendorf, Charles E. and Judy Conrad. 1991. “Hurricane Gold: Part I—The Loss.” Mariner’s Weather Log, Vol. 35, No. 3, 5-10. History of the sinking of the gold ship Central America and the subsequent discovery of its wreck.

Herodotus. 1972. The Histories. Translated by Aubrey de Selincourt. London: Penguin Books. A famous Greek tourist tells of his travels in the ancient world.

Homer. 1996. The Odyssey. Translated by Robert Fagles. New York: Penguin Putnam. A modern translation of Homer’s epic poem concerning Odysseus’ ten-year wanderings after the Trojan war.

IEEE 2002. Remote Sensing: Integrating our Views of the Planet. International Geoscience and Remote Sensing Symposium 2002, 24th Canadian Symposium on Remote Sensing, Toronto, June 24-28. Piscataway, New Jersey: The Institute of Electrical and Electronic Engineers. Description of the latest technologies for remote sensing of the environment of the oceans and continents

The Institute of Shipping Economics and Logistics (ISL) 2005. Available www.isl.org. Accessed 3/25/05. Various “Shipping Statistics and Market Review” summaries. An excellent source for merchant shipping statistics and data.

The International Association of Classification Societies. (IACS). Available www.iacs.org.uk. Accessed 6/19/05. Data concerning the member societies that make up the IACS. Purpose of the IACS.

Janssen, Peter. 2004. “Towards Freak-Wave Prediction Over the Global Oceans.” European Center for Medium-Range Weather Forecasts ECMWF Newsletter, No. 100, Spring 2004, 24-27. New developments in forecasting weather conditions that might be conducive to extreme wave formation.

Jenkins, Alastair D., et al. 2002. “Rogue Waves and Extreme Events in Measured Time Series.” Norwegian Meteorological Institute Report, No. 138, August. Bergen, Norway. Technical report, part of the European Community MaxWave research project, with more evidence for the existence of extreme waves.

Jenkins, Bruce. 1999.  North Shore Chronicles—Big-Wave Surfing in Hawaii. Rev. ed. Berkeley: Frog Ltd. Some people even go looking for extreme waves; this narrative tells the story of the world’s most accomplished surfers who have had intimate contact with waves large enough to crush modern ocean-going vessels.

Junger, Sebastian. 1997. The Perfect Storm—A True Story of Men Against the Sea. New York: W. W. Norton. The classic story of man trying to survive at sea in the presence of giant waves, with an explanation of one set of conditions that can unexpectedly produce extreme wave conditions.

Kane, Herb K. 1976. Voyage—The Discovery of Hawaii.  Honolulu: Island Heritage Books. Interesting history of ancient Polynesian navigation by a man who participated in the design, construction, and sailing of the Hokule’a from Hawaii to Tahiti.

Kinsman, Blair. 1965. Wind Waves—Their Generation and Propagation on the Ocean Surface. Englewood Cliffs, New Jersey: Prentice-Hall. A classic treatise on wind, waves, and how waves are formed—some material dated, but extremely well written and entertaining.

Kotsch, Rear Admiral William J. and Richard Henderson. 1984. The Heavy Weather Guide. 2nd ed. Annapolis: Naval Institute Press. A valuable reference book for merchant vessels encountering gales and heavy weather.

Knecht, G. Bruce. 2001. The Proving Ground. New York: Warner Books. Gripping account of the disastrous 1998 Sydney-Hobart race.

Krieger, Michael. 2002.  All the Men in the Sea: The Untold Story of One of the Greatest Rescues in History. New York: The Free Press.  Hundreds of oil field workers are on a barge in the Gulf of Mexico when it is hit by Hurricane Roxanne in 1995.

Lander, James F. and Patricia A. Lockridge. 1989. United States Tsunamis (including United States Possessions 1690–1988. National Geophysical Data Center, publication 41-2. Boulder, Colorado: U.S. Department of Commerce. Basic reference on United States tsunami.

Larson, Erik. 1999. Isaac’s Storm—A Man, a Time, and the Deadliest Hurricane in History. New York: Crown Publishers. The chilling story of the destruction of Galveston, Texas by storm surge and large waves.

LeBlond, Paul H. and Lawrence A. Mysak. 1978. Waves in the Ocean. New York: Elsevier. An outdated but classic review of wave theory.

Levathes, Louise. 1994. When China Ruled the Seas. New York: Simon & Schuster. The story of early Chinese navigators.

Lewis, David. 1979. We the Navigators—The Ancient Art of Land Finding in the Pacific. Honolulu: The University Press of Hawaii. Detailed description of ancient Polynesian navigation methods by a man who studied under one of the best surviving navigators.

Lochhaas, Tom, ed. 2003. Intrepid Voyagers—Stories of the World’s Most Adventurous Sailors. New York: International Marine/McGraw-Hill. A series of accounts of sailors who have sailed around the world alone, or crossed the oceans in the smallest boats, or otherwise have experienced the sea and its greatest challenges.

Mariner’s Weather Log. various issues. Stennis Space Center, Mississippi: U.S. Department of Commerce National Oceanic and Atmospheric Administration. A wealth of real-life experiences with extreme waves by the men and ships that experienced them, especially Vol. 29, 1985; Vol. 30, 1986; Vol. 37, 1993; April 2001.

Marriott, John. 1987. Disaster at Sea. London: Ian Allan. Accounts of various shipwrecks, including a description of the grounding of the Memphis.

Marx, Robert F. 1983. Shipwrecks in the Americas. New York: Bonanza Books. A history of many shipwrecks in the Americas, with a description of how wrecks are located and a section detailing the exploration of Port Royal, Jamaica

Massel, Stanislaw R. 1996. Ocean Surface Waves: Their Physics and Prediction. Singapore: World Scientific. A very comprehensive review of all of the mathematical theories used to model wind-wave interaction.

MaxWave Project. 2003. Research project no. EVK:3-2000-00544. Bergen: Commission of the European Communities. Available http://w3gkss.de/projects/maxwave. Accessed 11/5/04. Includes scope of work, scientific and technical objectives, work plan, selected technical reports, and a description of the tasks planned in this ambitious and important new research program aimed at improving our knowledge of extreme waves.

McAnally, William H., Jr. 1975. Los Angeles and Long Beach Harbors Model Study— Report 5: Tidal Verification and Base Circulation Tests. Waterways Experiment Station, U.S. Army Corps of Engineers, Report H-75-4, September. Description of the hydraulic model of Los Angeles and Long Beach Harbors.

Mercator 2005. Forecast of Container Vessel Specifications and Port Calls within San Pedro Bay. Bellevue, Washington: Mercator Transport Group. A study of container ship trends performed for the Port of Los Angeles.

Milbury, Jim. 2005. “Bering Sea Shipwreck Spill Threatens Alaskan Islands.” NOAA Report, Vol. xiv, No.1, 1. Description of the loss of the Selendang Ayu.

Morison, Samuel Eliot. 1978. The Great Explorers. Oxford: Oxford University Press. A history of Columbus and other early European explorers and the discovery of America.

Műller, Peter, ed. 2005. Rogue Waves. The 14th  ‘Aha Huliko’a Hawaiian Winter Workshop Proceedings.  Honolulu: University of Hawaii. Available at  http://www.soest.hawaii.edu/PubServices/AhaHulikoa.html. Accessed 10/3/05. A compendium of the state-of-the-art of  rogue wave research in 2005.

Műller, Peter, Chris Garrett and Al Osborne. 2005. “Rogue Waves—The 14th ‘Aha Huliko’a Hawaiian Winter Workshop.” Oceanography, Vol. 18, No. 3, September, 66-75.  This is the summary report of the aforementioned workshop.

Mundle, Rob. 1999. Fatal Storm—The Inside Story of the Tragic Sydney-Hobart Race. Camden, Maine: International Marine/McGraw Hill. Another account of the Sydney-Hobart race in 1998 as it was hit by a “weather bomb” with devastating results.

Myles, Douglas. 1985. The Great Wave. New York: McGraw-Hill. Tsunami incidents.

Naval History Division. 1979. Dictionary of American Naval Fighting Ships. Vol. V (letters N through Q). Washington D.C.: U.S. Navy Department. Battleship Pittsburgh incident in 1945 typhoon.

Ochi, Michel K. 1998. Ocean Waves—The Stochastic Approach. Cambridge: Cambridge University Press. A summary of modern wave science and the current methods of analyzing and predicting wave behavior.

——— 2003. Hurricane-Generated Seas. New York: Elsevier. A complete treatment of how hurricanes generate extreme waves.

Olagnon, M. and G.A. Athanassoulis, eds. 2001. Rogue Waves 2000. Proceedings of a workshop organized by Ifremer, November 29-30, 2000, Brest, France. An excellent compendium of recent research on modeling, and forecasting extreme waves.

Owens, Hugh 2004. “The Lituya Legacy.” Cruising World, October, 50-52. A little known, but huge tsunami caused by an earthquake induced landslide—remarkable in that there were surviving eye witnesses.

Pararas-Carayannis, George. 2005. “The Loss of the USS Memphis on 29 August 1916—Was a Tsunami Responsible?” Available http://drgeorgepc.com/LossUSSMemphis1.hmtl. Accessed 7/05. This well-documented study demonstrates that it was most likely swell from hurricanes rather than a tsunami that wrecked the Memphis.

Pardey, Lin and Larry Pardey. 1996. Storm Tactics—Modern Methods of Heaving-to for Survival in Extreme Conditions. Arcata, California: Paradise Cay Publications. A valuable handbook for the small boat sailor planning to venture off-shore.

Parry, John H. 1981. The Discovery of the Sea. Berkeley: University of California Press. Description of the earliest sailors including a history of the Chinese navigators.

Prager, Ellen J. 2000. The Oceans. New York: McGraw-Hill. A beautiful, almost poetic treatment of oceans and oceanography.

Preston, Diana and Michael Preston. 2004. A Pirate of Exquisite Mind—Explorer, Naturalist and Buccaneer: The Life of William Dampier. New York: Walker and Company. Describes Dampier’s circumnavigations and many contributions to our knowledge of the oceans.

Price, A. Grenfell, ed. 1990. The Explorations of Captain James Cook in the Pacific—As Told by Selections of His Own Journal 1768-1779. New York: Dover Publications. Cook’s discoveries in his own words.

Ray, Thomas. 1965. “A History of Texas Towers in Air Defense, 1952-1964.” Washington D.C.: Air Defense Command (ADC) Historical Document 29. Description of the Texas Towers construction program including purpose, how they were built and the disaster that befell tower number 4.

Rhodius, Apollonius. 1998. Translated by Richard Hunter. Jason and the Golden Fleece—The Argonautica. Oxford: Oxford University Press. Retelling of the ancient Greek legend of Jason and his quest for the Golden Fleece that would entitle him to rule in his own right.

Ritchie, David. 1996. Shipwrecks—An Encyclopedia of the World’s Worst Disasters at Sea. New York: Checkmark Books. This book has capsule descriptions of hundreds of sea disasters listed in alphabetical order, including a number of those cited in this book such as Poet, Grand Zenith, and so on.

Rosenthal, Wolfgang. No date. MaxWave Rogue Waves—Forecast and Impact on Marine Structures. Available http://w3g.gkss.de/projects/maxwave/workp/WP1.pdf. Accessed 11/5/04. Incomplete working paper.

Rousmaniere, John. 1983. The Annapolis Book of Seamanship.  New York: Simon and Schuster. A standard guide for sailors in the handling of small craft in rough weather.

Royal Commission on the Ocean Ranger Disaster. 1984. Hearings—Royal Commission on the Ocean Ranger Marine Disaster. Toronto, Canada. The official account of the Ocean Ranger disaster.

Sarpkaya, Turgut, and Michael Isaacson. 1981. Mechanics of Wave Forces on Offshore Structures. New York: Van Nostrand Rheinhold. Discusses engineering methods for determining wind, wave, and other loads on offshore structures.

Science News. 2005. Vol. 167, No. 24,  June 11, 382. Underwater rogue wave measurements off of Florida during Hurricane Ivan.

Shaw, David. 2005. “Badly Caught Out, with Tragic Consequences.” Cruising World, July, 18. Rogue wave causes 45-foot Hardin cutter-ketch to founder.

Sheets, Bob, and Jack William. 2001. Hurricane Watch—Forecasting the Deadliest Storms on Earth. New York: Vintage Books. A highly recommended book on how hurricanes are formed and describing the history of hurricane forecasting.

Simpson, Robert H. and Herbert Riehl. 1981. The Hurricane and Its Impact. Baton Rouge: Louisiana State University Press. A classic treatment of hurricanes by one of the men responsible for the Saffir/Simpson Hurricane Scale.

Sverdrup, Keith A., Alyn C. Duxbury and Alison B. Duxbury. 2005. An Introduction to the World’s Oceans. 8th ed. New York: McGraw Hill. A first rate book for an overall treatment of oceanography.

Tarman, Daniel, and Edgar Heitmann. No date. “Case Study II. Derbyshire—Loss of a Bulk Carrier.” Ship Structure Committee. http:www.shipstructure.org/derby.shtml. Accessed 6/10/05. A structural analysis of possible Derbyshire failure modes.

Taviani, Paolo Emilio. 1989. Columbus, The Great Adventure—His life, His Times, and His Voyage. Translated by Luciano E. Farina and Marc A. Beckwith. New York: Crown Publishers/Orion Books. Review of Columbus and the discovery of America.

Thomas, Steve. 1997. The Last Navigator. Camden, Maine: International Marine. Story about techniques of ancient Polynesian navigators.

Thompson, Dick. 2004. “Rogue Waves Revealed.” Boats U.S. Magazine, November, 34-35. A summary of some of the new findings on extreme waves.

——— 2005. “Roughed Up by Rogue Waves.” Boat U.S. Magazine, September, 26-27. Accounts of recent boat sinkings.

Thompson, Tommy. 1998. America’s Lost Treasure. New York: The Atlantic Monthly Press. The amazing story of the discovery and recovery of cargo from the Central America, also known as “The Ship of Gold,” carrying a cargo of gold bullion and the gold rush miners who had found it, and lost it in a violent storm in 1857.

Trumbull, Robert. 1942. The Raft. Camden, New Jersey: Henry Holt. The inspiring story of a naval air crew that crash land in the Pacific during World War II and survive by ingenuity in a small raft.

U.S. Navy. 1976. Dictionary of American Naval Fighting Ships. Vol. I-VII. Washington D.C.: Naval Historical Division, Department of the Navy. Lists every major navy ship and gives a short history and description of the vessel.

Van Dorn, William G. 1977. Oceanography and Seamanship. New York: Dodd, Mead and Company. Another excellent book on oceans and seamanship. A newer edition of this book is available.

Walker, Spike. 2001. Coming Back Alive—The True Story of the Most Harrowing Search and Rescue Mission Ever Attempted on Alaska’s High Seas. New York: St. Martin’s Press. The story of the U.S. Coast Guard rescue of the crew of the fishing vessel La Conte.

Warshaw, Matt. 2003. The Encyclopedia of Surfing. New York: Harcourt. Everything you could possibly want to know about surfing may be found here.

Wilson, James F., ed. 1984. Dynamics of Offshore Structures. New York: John Wiley & Sons. Engineering methods for the dynamic analysis of offshore structures.

Winchester, Simon. 2004. Krakatoa—The Day the World Exploded. New York: Perennial Books. The dramatic story of the island that blew up, and the devastating tsunami that followed.

World Meteorological Organization. 1988. Guide to Wave Analysis and Forecasting. Geneva: World Meteorological Organization, WMO-702. The classic guide to forecasting sea conditions.

Young, Ian R. 1999. Wind Generated Ocean Waves. Oxford: Elsevier. A comprehensive review of wind-wave analytical methods and theory including wave measurements.

Zebrowski, Ernest, Jr. 1997. Perils of a Restless Planet—Scientific Perspectives on Natural Disasters. London: Cambridge University Press. A review of natural disasters (storms, earthquakes, tsunami, volcanoes, asteroid impacts) and their potential or actual impact on life on earth.

End Notes for the excerpts listed above.
Note: Refer to the annotated bibliography for the complete citation.

[1] Herodotus (1972), 283.

[2] Parry (1981), 39–40.

[3] Bergreen (2004), 232–238.

[4] Dyson (1991), 64. See also Taviani (1989) and Morrison, (1978), 351–548.

[5] Morrison (1978), 370.

[6] Cummins (1992), 79–133.

[7] Bergreen (2004), 132–171. See also Louise Levathes (1994), When China Ruled the Seas. New York: Simon & Schuster.

[8] Bergreen (2004), 391–392.

[9] Ochi (1998), 58; Young (1999), 25.

[10] After Bruce J. Muga, “Statistical Descriptions of Ocean Waves” Chapter 6 in Wilson, ed. (1984), 159.

[11] Muga (1984), 159–161; Young (1999), 26.

[12] Young (1999), 27. Note: be warned that in spite of this, the largest wave can be the third, the ninth, the tenth, et cetera.

[13] Muga (1984), 160.

[14] Van Dorn (1974), 192–199.

[15] Ochi (1998), 255–280.

[16] Young (1994), 40.

[17] See Sheets and Williams (2001), 285-286.

[18] Source: U.S. NOAA, National Weather Service, National Hurricane Center web Site at: www.nhc.noaa.gov.

[19] Ochi (2003), 16.

[20] Ibid., 83–85.

[21] Ibid., 27.

[22] Ibid., 148.

[23] Source: Adapted from Ochi (2003), 19.

[24] See Sheets and Williams (2001), 203–221. For the National Hurricane Center Web site, go to www.nhc.noaa.gov.

[25] World Meteorological Organization (1988), 2–4.

[26] Price, ed. (1960), 43.

[27] Lewis (1979).

[28] Thomas (1997).

[29] Ibid., 81.

[30] Lewis (1979), 200–203.

[31] This was accomplished under the auspices of the Polynesian Voyaging Society, formed in 1973 by Ben Finney, Herb Kane, and Tommy Holmes. See http://pvs.kcc.hawaii.edu.

[32] Finney (1994).

[33] Bascom (1980), 95–111. Chapter 5, “Tides and Seiches.” This small book has one of the clearest descriptions of tidal behavior that I’ve encountered, and in other respects is a remarkable book. It has been out of print for some time.

[34]  LeBlond (1978), 510.

[35] Bascom (1980), 99.

[36] Sverdrup et al. (2005), 286–287.

[37] Bascom (1980), 108.

[38] Ralph Vartbedian and Peter Pae (2005), “A Barrier That could Have Been,” Los Angeles Times, Friday September 9, A10.

[39] Jane Hollingsworth (1989), “The Chicago Seiches” Mariners Weather Log, Vol. 3, No. 2, spring, 16–19.

[40] LeBlond (1978), 512.

[41] Sverdup et al. (2005), 289–290.

[42] Bascom (1980), 103–104.

[43] Ibid., 104.

Chapter 10 End Notes

[44]Mercator (2005). Forecast of Container Vessel Specifications and Port Calls within San Pedro Bay. Bellevue, Washington: Mercator Transport Group

[45] Mercator (2005), 5-10, op. cit.

[46] Tarman and Heitman (no date) 8.

[47] Ibid., 9.

[48] Ibid., 12–13.

[49] Ibid., 14–15.

[50] Sverdrup et al., (2005), 252.

[51] Ibid., 256.

[52] Bryant (2001), 50.

[53] Sverdrup et al., (2005), 289.

[54] Personal communication, Craig B. Smith with Professor Chris Garrett, University of Victoria, British Columbia, October 5, 2005.

[55] For those interested in more detail, Bruce J. Muga, “Deterministic Descriptions of Ocean Waves,” Chapter 2 in Wilson ed. (1984), provides an excellent overview.

[56] Bruce J. Muga,. “Statistical Descriptions of Ocean Waves,” Chapter 6 in Wilson, ed. (1984).

[57] Bitner-Gregersen (2002), 95.

[58] Ibid., 100.

[59] Personal communication, Craig B. Smith with Professor Chris Garrett, University of Victoria, British Columbia, October 5, 2005. See also Müller, Garrett, and Osborne (2005), 68-69.

[60] This is known as Hooke’s Law. The constant of proportionality between stress and strain is known as Young’s modulus.

[61] Paul H Taylor and Christopher Swan, (2000) “New Waves, Solitons, and Spreading,” in Olagnon and Athanassoulis, eds. (2001), 245-254.

[62] Kristian B. Dysthe, (2000) “Modeling a Rogue Wave—Speculations or a Realistic Possibility?” in Olagnon and Athanassoulis, eds. (2001), 255-264.

[63]Efim Pelinovski, et al., (2000) “Nonlinear Wave focusing as a Mechanism of the Freak Wave Generation in the Ocean,” in Olagnon and Athanassoulis, eds. (2001), 193-204.

[64] Peter Janssen “Nonlinear four-wave interaction and freak waves” in Müller, ed. (2005), 85-90.

[65] Kristian B. Dysthe, (2000) “Modeling a Rogue Wave—Speculations or a Realistic Possibility?” in Olagnon and Athanassoulis, eds. (2001), 255-264; also in the same reference: Miguel Onorato, et al., “Occurrence of Freak Waves from Envelope Equations in Random Ocean Wave Simulations,”181 and Efim Pelinovski, et al., “Nonlinear Wave Focusing as a Mechanism of the Freak Wave Generation in the Ocean,” 193-204.

[66] Douglas Faulkner, “Rogue Waves—Defining their Characteristics for Marine Design,” in Olagnon and Athanassoulis, eds. (2001), 9.

[67] Peter Gorf, et al., “Bow Damage in Steep Waves” in Olagnon and Athanassoulis, eds. (2001), 38-39.