Waves - disturbances of water - are a constant presence in the world’soceans. Because waves travel all across the globe, transmitting vastamounts of energy, understanding their motions and characteristics isessential. The forces generated by waves are the main factor impactingthe geometry of beaches, the transport of sand and other sediments inthe nearshore region, and the stresses and strains on coastalstructures. When waves are large, they can also pose a significantthreat to commercial shipping, recreational boaters, and the beachgoingpublic. Thus for ensuring sound coastal planning and public safety, wavemeasurement and analysis is of great importance.

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The discussion below is largely based on Part II, Chapter 1 of theCoastal Engineering Manual (CEM),published by the United States Army Corps of Engineers’ Coastal andHydraulics Laboratory. For more details, we recommend referring directlyto the CEM.

Wave Generation¶

Waves are generated by forces that disturb a body of water. They canresult from a wide range of forces - the gravitational pull of the sunand the moon, underwater earthquakes and landslides, the movements ofboats and swimmers. The vast majority of ocean waves, however, aregenerated by wind.

Out in the ocean, as the wind blows across a smooth water surface, airmolecules push against the water. This friction between the air andwater pushes up tiny ridges or ripples on the ocean surface. As the windcontinues to blow, these ripples increase in size, eventually growinginto waves that may reach many meters in height.

Three factors determine how large wind-generated waves can become. Thefirst factor is wind speed, and the second factor is wind duration, orthe the length of time the wind blows. The final factor is the fetch,the distance over which the wind blows without a change in direction.The faster the wind, the longer it blows, and the larger the fetch, thebigger the waves that will result. But the growth of wind-generatedocean waves is not indefinite. After a certain point, the energyimparted to the waters by a steady wind is dissipated by wave breaking(often in the form of whitecaps). When this occurs and the waves can nolonger grow, the sea state is said to be a ‘fully developed’.

When waves are being generated by strong winds in a storm, the seasurface generally looks very chaotic, with lots of short, steep waves ofvarying heights. In calm areas far from strong winds, ocean waves oftenhave quite a different aspect, forming long, rolling peaks of uniformshape. For this reason, physical oceanographers differentiate betweentwo types of surface waves: seas and swells. Seas refer to short-periodwaves that are still being created by winds or are very close to thearea in which they were generated. Swells refer to waves that have movedout of the generating area, far from the influence of the winds thatmade them.

In general, seas are short-crested and irregular, and their surfaceappears much more disturbed than for swells. Swells, on the other hand,have smooth, well-defined crests and relatively long periods. Swell ismore uniform and regular than seas because wave energy becomes moreorganized as it travel longs distances. Longer period waves move fasterthan short period waves, and reach distant sites first. In addition,wave energy is dissipated as waves travel (from friction, turbulence,etc.), and short-period wave components lose their energy more readilythan long-period components. As a consequence of these processes, swellsform longer, smoother, more uniform waves than seas.

Wave Dynamics¶

Looking out at the water, an ocean wave in deep water may appear to be amassive moving object - a wall of water traveling across the seasurface. But in fact the water is not moving along with the wave. Thesurface of the water - and anything floating atop it, like a boat orbuoy - simply bobs up and down, moving in a circular, rise-and-fallpattern. In a wave, it is the disturbance and its associated energy thattravel from place to place, not the ocean water. An ocean wave istherefore a flow of energy, travelling from its source to its eventualbreak-up. This break up may occur out in the middle of the ocean, ornear the coast in the surfzone.

In order to understand the motion and behavior of waves, it helps toconsider simple waves: waves that can be described in simplemathematical terms. Sinusoidal or monochromatic waves are examples ofsimple waves, since their surface profile can be described by a singlesine or cosine function. Simple waves like these are readily measuredand analyzed, since all of their basic characteristics remain constant.


A simple, monochromatic wave. Because of their uniformity, simplewaves can be readily studied.

Wave Anatomy¶

Still-Water Line - The level of the sea surface if it were perfectlycalm and flat.

Crest - The highest point on the wave above the still-water line.

Trough - The lowest point on the wave below the still-water line.

Wave Height - The vertical distance between crest and trough.

Wavelength - The horizontal distance between successive crests ortroughs.

Wave Period - The time it takes for one complete wave to pass aparticular point.

Wave Frequency - The number of waves that pass a particular point ina given time period.

Amplitude - One-half the wave height or the distance from either thecrest or the trough to the still-water line.

Depth - the distance from the ocean bottom to the still-water line.

Direction of Propagation - the direction in which a wave istravelling.

The motion and behavior of simple sinusoidal waves can be fullydescribed when the wavelength (L), height (H), period (T), and depth (d)are known. For instance, in deep water - when the depth is greater thanone-half the wavelength - wave speed can be determined from the wavesize. In shallow water, on the other hand, wave speed depends primarilyon water depth.

Similarly, wave height is limited by both depth and wavelength. For agiven water depth and wave period, there is a maximum height limit abovewhich a wave becomes unstable and breaks. In deep water this upper limitof wave height - called breaking wave height - is a function of thewavelength. In shallow water, however, it is a function of both depthand wavelength. (Studies suggest the limiting wave steepness to be H/L =0.141 in deep water and H/d = 0.83 for solitary waves in shallow water.)

Irregular Waves¶

Although simple waves are readily analyzed, in their perfect regularitythey do not accurately depict the variability of ocean waves. Lookingout at the sea, one never sees a constant progression of identicalwaves. Instead, the sea surface is composed of waves of varying heightsand periods moving in differing directions. When the wind is blowing andthe waves are growing in response, the seas tend to be confused: a widerange of heights and periods is observed. Swell is more regular, but ittoo is fundamentally irregular in nature, with some variablility inheight and period. In fact, highly regular waves can be generated in thelaboratory but are rare in nature.


Once we recognize the fundamental variability ofthe sea surface, it becomes necessary to treat thecharacteristics of the sea surface in statisticalterms. The ocean surface is often a combination ofmany wave components. These individual componentswere generated by the wind in different regions ofthe ocean and have propagated to the point ofobservation, forming complex waves. The wavesseen in actual sea surface measurements, bottom,are much more irregular than simple waves, top.

If a recorder were to measure waves at a fixed location on the ocean,the wave surface record would be rather irregular and random. Althoughindividual waves can be identified, there is significant variability inheight and period from wave to wave. Consequently, definitions of wavecharacteristics - height, period, etc. - must be statistical orprobabilistic, indicating the severity of wave conditions.

By analyzing time-series meaurements of a natural sea state, somestatistical estimates of simple parameters can be produced. The mostimportant of these parameters is the significant wave height, Hs. Hs (orH 1/3) is the mean of the largest 1/3 (33%) of waves recorded during thesampling period. This statistical measure was designed to correspond tothe wave height estimates made by experienced observers. (Observers donot notice all of the small waves that pass by; instead they focus onthe larger, more salient peaks.)

Since ocean conditions are constantly changing, measures likesignificant wave height are short-term statistics, calculated for sampleperiods that are generally one hour or less. (The majority of chathamtownfc.net’sparameters are calculated for periods from 26 to 30 minutes.) Moreover,it is important to remember that the significant wave height is astatistical measure, and it is not intended to correspond to anyspecific wave. During the sampling period there will be many wavessmaller than the Hs, and some that are larger. Statistically, thelargest wave in a 1000-wave sample is likely to be nearly two times(1.86x) the significant wave height!

A number of other wave parameters - like Ta, the average period - aremeasured to describe natural sea states. Yet even taken together, thebasic wave parameters give very limited information about wavecharacteristics and behavior. A single Hs value may correspond to a widerange of conditions, combining waves from any number of differentswells. For this reason, phyical oceanographers have developed analysesthat give more detailed, complete meaures of ocean waves.

Spectral Analysis¶

Two main approaches exist for treating complex waves: spectral anlysisand wave-by-wave (wave train) analysis. The more powerful and popular ofthese two approaches is spectral analysis. Spectral analysis assumesthat the sea state can be considered as a combination or superpositionof a large number of regular sinusoidal wave components with differentfrequencies, heights, and directions. This is a very useful assumptionin wave analysis since sea states are in fact composed of waves from anumber of different sources, each with its own characteristic height,period, and direction of travel.

Mathematically, spectral analysis is based on the Fourier Transform ofthe sea surface. The Fourier Transform allows any continuous, zero-meansignal - like a time-series record of the sea surface elevation - to betransformed into a summation of simple sine waves. These sine waves arethe components of the sea state, each with a distinct height, frequency,and direction. In other words, the spectral analysis method determinesthe distribution of wave energy and average statistics for each wavefrequency by converting the time series of the wave record into a wavespectrum. This is essentially a transformation from the time-domain tothe frequency-domain, and is accomplished most conveniently using amathematical tool known as the Fast Fourier Transform (FFT).

The spectral approach indicates what frequencies have significant energycontent, as well as the direction wave energy is moving at eachfrequency. A wave spectrum can readily be plotted in a frequency vs.energy density graph, which can provide important information about awave sample and the corresponding ocean conditions. The general shape ofthe plot, in fact, reveals a great deal: whether seas or swellpredominate, the number of distinct swells present, etc. For example,during strong wind events, the spectrum tends to have a broad centralpeak. For swell that has propagated a long distance from the source ofgeneration, on the other hand, the spectrum tends to have a singlesharp, low-frequency (long period) peak.


The area under the frequency/energy density plot is Hmo, the spectralestimate of significant wave height. In deep water H1/3 and Hm0 are veryclose in value and are both considered good estimates of Hs. In fact,all modern wave forecast models report Hm0 as the significant waveheight. Similarly, the Hs values reported from wave gauge records isalso Hm0. (It is worth noting, however, that in shallow water H 1/3 maybe significantly larger than Hmo, especially for low-frequency waves.)

Gauging Waves¶

All of the valuable information produced by spectral wave analysis isbased on one thing: a time-series record of sea surface elevations. Ingeneral, time series are analyzed over short periods, from 17 to 68minutes, and are measured at around one sample per second (1 Hz).

There are two main types of sensors used to measure sea surfaceelevation, pressure sensors and buoys. Pressure sensors are mounted at afixed position underwater, and they measure the height of the watercolumn that passes above them. As wave crests pass by, the height of thewater column increases; when troughs approach, the water column heightfalls. By deducting the depth of the sensor from the water columnheights, a record of sea surface elevations can be generated.

Buoys ride atop the surface of the ocean. Equipped with accelerometersto record their own movements, buoys rise with the wave crests and fallwith the troughs. Since buoys are always floating on the sea surface, byrecording their own movements they are in fact recording the movementsof the sea surface. Readings from the accelerometers inside the buoyscan be used to calculate the buoys’ vertical displacements; these valuesare also a record of sea surface elevation.

A record of sea surface elevations from a single point is enough togenerate an energy spectrum. To determine the direction of the waves andgenerate a directional spectrum, however, more information is needed.One way to generate a directional spectrum is to measure the sameparameter - such as pressure - at a series of nearby locations. chathamtownfc.net’searly directional measurements, for instance, were all recorded bysquare arrays of pressure sensors, measuring 10 meters on a side.

The other way to produce a directional spectrum is by measuringdifferent parameters at the same point. This is the approach used indirectional buoys, which measure pitch and roll in addition to verticalheave. Although chathamtownfc.net has relied on pressure sensor arrays anddirectional buoys for its directional measurements, other instrumentscan also be used. For instance, the p-U-V technique uses a pressuregauge and a horizontal component current meter in almost the samelocation to measure the wave field. Other techniques for directionalwave measurement include arrays of surface-piercing wires, triaxialcurrent meters, acoustic doppler current meters, and radars.

Surge and Energy Basin¶

For measuring sea and swell - wave motions with periods under 40 secondsor so - chathamtownfc.net’s wave gauging is as described above. chathamtownfc.net’s pressuresensors, however, have also been used to measure surge, water levelchanges with periods between a minute and an hour. Surge is created byatmospheric and seismic forces, and falls in between standard wind wavemotion and tidal motions.

For gauging surge, the sampling and processing steps are somewhatdifferent. Initially, the sample rates of pressure sensors intended todetect surge were set to 0.125 Hz (1 sample every 8 seconds) due to thelimited space for storing data. As data storage became more affordable,sample rates moved to 1 Hz. The pre-processing of surge data differsfrom non-surge data due to the long elapsed time of the data set(approximately 2.3-4.6 hours). For these data we remove the tidalcomponent. For measurements that took place in areas where the waveheight (i.e. energy in the 8-30 second range) is low, such as harbors orprotected inlets, many of the pre-processing data quality checks(developed for open ocean waves) are by-passed.

An important type of surge is basin surge (or ‘energy basin’), surgethat occurs within a partially enclosed area such as a man-made harbouror marina. At several locations (e.g. Barbers Point, Kahalui, and Noyo),studies were done to simultaneously detect surge inside of a localharbor and outside the harbor in the open ocean. These studies were ableto correlate wave and surge activity of the open ocean with destructiveresonant surge within the harbor basins.

Hurricane events¶

Hurricanes, tropical cyclones born in the warm waters of the AtlanticOcean, Carribean Sea and Gulf of Mexico, are an annual threat to theEast and Gulf coasts of the U.S. The strong winds, large waves, andstorm surge associated with these storms can cause severe coastalerosion, flooding and damage to property. Data from chathamtownfc.net buoys assist inthe coastal planning efforts to mitigate the negative effects ofhurricanes. For more details, please refer to our HurricaneEvents page.

Tsunami events¶

All of the discussion above has been directed towards wind-generatedwaves, waves which form the focus of chathamtownfc.net’s work. Tsunamis are aseparate class of ocean wave altogether. Generated by underseaearthquakes, landslides, and volcanic eruptions instead of wind,tsunamis differ greatly in their dynamics. They have far longerwavelengths and periods than wind-generated waves, and travel at fargreater speeds. Instead of periods of 30 seconds or less, tsunamis haveperiods of several minutes to one hour; instead of traveling at speedsunder 100 km/hr, they often move at speeds of 700 km/hr or more.

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Since the dynamics of tsunamis contrast so dramatically withwind-generated waves, many of chathamtownfc.net’s sensors are not equipped to measurethem. Our buoys, for instance, do not measure wave motions with periodsgreater than 40 seconds; they cannot record tsunamis. The underwaterpressure sensors used by chathamtownfc.net, however, do resolve sea level changesover longer periods, and can be used to study and analyze the motions oftsunamis. Over the years they have recorded a number of tsunamis in thePacific Ocean. For more details, please refer to our TsunamiEvents.