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Ocean Waves (continued) In shallower water, Stokes drift contributes to sediment transport onto beaches and along beaches when the waves approach the coast at an angle. Shoaling and breaking Waves approaching the shore from the open ocean are affected in several ways. As they become shallow-water waves, velocity C decreases with decreasing water depth h [Eq. ( 4 )]. Consequently, waves approaching the shore at an angle are refracted so their crests are brought nearly parallel to the shore- line. Wave period T does not change as h decreases, so wave- length L = CT must decrease according to Eq. ( 4 ). Shallowing also causes a growth in wave height as in relation ( 9 ), where the value of r depends on the character of the waves. For example, in the absence of dissipation, r = 1/4 according to linear theory for shallow-water waves, while r = 1 for solitary waves of moderate amplitude. As wave height grows, nonlinear terms in the equations of motion become significant. At first, this results in a verti- cal asymmetry in the wave shape, with crests becoming more peaked and troughs more rounded. Then, as the wave moves into shallow water, a strong horizontal asymmetry develops in which the forward face of the wave becomes progressively steeper than the backward face. This process typically contin- ues until the wave breaks. The resulting breakers can have a variety of forms (collapsing, plunging, surging, and so forth), depending on the height of the entering waves and the slope of the seabed. A rough criterion for breaking is shown in rela- tion ( 10 ), or, using Eq. ( 4 ) for shallow water, H > h. In the open ocean also, waves often break. In this case, the criterion becomes H > 1/k [using Eq. ( 4 ) for deep water]. White- caps from deep-water breaking waves begin to appear at wind speeds of about 0.45 m/s (10 mi/h), while at wind speeds above 27 m/s (60 mi/h) all the high waves are breaking. Wave measurement There are three classes of instruments for measuring ocean surface waves: those which are at the air-sea interface, those which are below it, and those which are above it. Because so many techniques can be used, only a few typical examples of each class will be described. At the surface Ocean surface waves can be measured from a dock with a wave staff held vertically in the water. The varying position η(t) of the sea surface on the staff is sensed in a variety of ways, for example, by seawater-shorting of the submerged part of a resistance wire wound along the staff. An accelerometer-instrumented buoy on a slack mooring line can provide a record of η(t) by double integration of the vertical acceleration. If, in addition, the buoy contains tilt sen- sors, it is capable of providing the directional spectrum S (f,θ) of the waves. Typically, data from a wave-measuring buoy are telemetered to a receiving station on shore. Below the surface The most common instrument of this class is the subsurface pressure sensor. The pressure measurement must be made at a level deep enough that it is always submerged; this has the advantage of reducing vulnerability to damage by ships and breaking waves. The main disadvantage of the method is the need to compensate for the frequency-dependent depth at- tenuation of the measured wave-induced pressure signal p(t) in converting it to surface elevation η(t). A narrow-beam inverted echo sounder can also be used to make subsurface wave measurements. It is placed on the sea- floor and directed upward, so the acoustic echo time from the surface is a measure of sea-surface elevation. But variations in temperature and salinity affect the speed of sound in water and hence affect instrument calibration. Also, bubbles in the water can cause spurious acoustic reflections. Above the surface Ground-based high-frequency (3–30 MHz) radar systems can provide information on wave height and direction from the backscattered signal. Ranges of 50–500 km (30–300 mi) are feasible, but with over-the-horizon sky-wave systems relying on ionospheric reflection, ranges beyond 3200 km (2000 mi) have been achieved. From aircraft, stereo-photographs can be taken of the sea surface and analyzed photogrammetrically, but this is a labori- ous process. Also, laser or narrow-beam radar ranging may be used to measure profiles of the sea surface. Two radar techniques are presently used for wave measure- ments from satellites. The radar altimeter (13.5 GHz) observes the reflection of pulses directed vertically. The deformation of the reflected pulse carries information about significant wave height H 1/3 in the irradiated patch of ocean (several kilome- ters in diameter). The synthetic-aperture radar (SAR; >1 GHz) obliquely irradiates a patch of ocean surface (about 100 km or 60 mi in size) and uses pulse timing and phase information in + ward ' s science Eq. (9) Eq. (10)