The Datawell Waverider

The MkIII's hull is a sphere of stainless steel 0.9 m across; with its batteries, antennas and chain, it weighs about 225 kg. Datawell gives 62 N of buoyancy for each centimeter it sinks. From its weight, the waterline comes about 5 cm above the widest point, where a rubber fender 1.00 m across surrounds it. CDIP paints its hulls yellow, with a maroon fender. A smaller hull, 0.7 m across, carries batteries for one year instead of three; three of Bluegraph's MkIIIs, all in the Great Lakes, are that size.

A hatch cover 475 mm across, held by 24 bolts, closes the top, and the antennas fit into ports in it: a yellow dome for GPS, a black dome for Iridium, and a whip on a spring for the HF radio, with the light at its tip. When daylight falls below 60 lux, the light flashes yellow, five times in ten seconds every twenty seconds, and can be seen about 4 nautical miles away. Datawell calls the whip a quarter-wave antenna, which at the HF link's frequencies makes it 2.1 to 2.9 m long; the figure draws it at 2.2 m, as CDIP's photographs show it. Buoys without the HF link can carry a shorter whip with only the light. Two handles are welded to the upper half of the hull, and a sickle-shaped mooring eye is underneath.

Inside, two rings of battery cells, in three sections of 15, each cell 65 mm across and 205 mm long, stand around an aluminum canister that runs down to the bottom of the hull and holds the motion sensor. The electronics unit hangs under the hatch cover. The figure places these parts from the manual's drawings and draws the cells evenly spaced.

CDIP's mooring for water 60 to 200 m deep starts under the hull with a shackle, an aluminum anode, 2 m of 3/8-inch stainless steel chain, a second anode and a swivel. Then come 30 m of rubber cord, polypropylene line with floats and sinkers, an acoustic release and the anchor chain. The anodes corrode instead of the steel, the chain steadies the buoy, and the swivel lets it turn without twisting the line. The whole line is about twice as long as the water is deep: off Torrey Pines, 1,128 m of line in 572 m of water.

The rubber cord, 35 mm thick for the 0.9 m hull, is what lets the buoy measure direction. A stiff line would hold the buoy back from the water's horizontal motion, more along the line than across it, and the buoy's direction of motion would differ from the water's. The cord stretches so easily that the buoy rides any wave whose frequency is well above the mooring's own natural frequency just as the water does: Datawell gives the mooring's pull, as a fraction of the wave's, as the square of the ratio of the two frequencies. The cord still holds the buoy in currents of up to 3 m/s.

As a wave passes in deep water, each particle of water near the surface moves around a circle in the plane of the wave's travel: forward under the crest, back under the trough, once each wave period. At the surface, the circle is as wide as the wave is high; deeper down it shrinks, by half for every 11 m under an 8-second swell. Rising and falling and moving back and forth are one motion.

A Waverider weighs as much as the water it displaces, so the water's forces carry it around the same circle, and its soft mooring barely holds it back. Datawell calls this orbit following. The buoy records how it moves: up and down, and toward north and west. A disk-shaped buoy, such as NOAA's 3-meter discus, is the other kind, slope following: it calculates direction from how its hull tilts with the slope of the water as it rises and falls. The Waverider tilts too, and measures its tilt, but only to convert its horizontal accelerations into true north and west.

There is a limit at the short end: when a wave is shorter than the hull's circumference, about 2.8 m, the buoy no longer follows it. The figure traces the path of the buoy's center over the last 8 seconds. Under the swell alone, the path is a circle 1.8 m across, the swell's height; the wind sea adds smaller, faster loops. Two particles of water beside the chain, 0.9 m and 1.7 m down, circle in step with it.

Low in the canister is Datawell's stabilized platform: a disk suspended in a fluid of the same density inside a plastic sphere, made sensitive to gravity by a small weight. It is a pendulum with a natural period of 40 s, as slow as a pendulum 400 m long, so it stays almost level however the buoy moves. An accelerometer on the disk measures the vertical acceleration, or heave.

Coils around the sphere measure the hull's pitch and roll directly. Two horizontal accelerometers, at right angles to each other, are fixed to the hull in a small stainless steel can, and a three-axis fluxgate compass gives the heading. Using the pitch, roll and heading, the buoy converts the accelerometers' readings into acceleration toward north and toward west.

The sensors are sampled 3.84 times a second. On board, the accelerations are filtered and converted into displacements (north, west and up) 1.28 times a second. Datawell gives heave from −20 m to +20 m, to 1 cm, within 0.5% after calibration, for waves of 1.6 to 30 s. The DWR4 has the same sensor, sampled faster, and follows waves with periods down to 1 s.

Every half hour, the buoy turns its record into spectra on board: 256 displacements (200 s) at a time, with eight of these averaged over 1,600 s. NDBC publishes the result in 64 frequency bands from 0.025 Hz to 0.58 Hz (periods of 40 s down to about 1.7 s), 0.005 Hz wide up to 0.1 Hz and 0.01 Hz wide above that. A DWR4's files have up to 98 bands, reaching about 0.96 Hz.

Direction comes from the three displacements together. At each frequency, the cross-spectra of heave with north and with west give the first four coefficients of the directional distribution, and from them a mean direction and a measure of spread, which NDBC publishes as α1, α2, r1 and r2, as it does for its own buoys. In deep water, where the orbits are circles, a buoy that follows the water moves as far horizontally as vertically. The check factor is the ratio of the two at each frequency, and CDIP issues a warning when it is above 2 in more than a quarter of the bands, a sign that something is keeping the buoy from following the water. Wave Intelligence separates the wave systems in these spectra.

A sensor in a pocket inside the mooring eye, about 45 cm below the surface, measures the sea's temperature from −5 to 46 °C, to 0.05 °C. Datawell gives its accuracy as 0.2 °C and its drift as less than 0.1 °C a year. CDIP checks each sensor to within 0.5 °C before the buoy is deployed.

CDIP's Waveriders report by Iridium satellite every 30 minutes to Scripps. CDIP also manages the data from wave buoys that other agencies operate, which is why 75 of Bluegraph's 77 appear in its files. NDBC publishes them under the buoys' five-digit station numbers. Where a shore station is within about 10 miles, the HF radio link (25.5 to 35.5 MHz, with a range of about 50 km over the sea) serves as a backup. The buoy also writes its data to a memory card on board, which fills any gaps once the buoy is recovered. CDIP replaces its buoys every two to three years.

Bluegraph reads these buoys from NDBC's files. The standard file gives wave height, the dominant and average periods, the mean direction and the sea temperature; the spectral summary gives the swell's and the wind sea's heights, periods and directions; the spectral files give the energy and the four direction coefficients in each band. A Waverider has no weather sensors, so these stations show no wind, air temperature or pressure.

CDIP's files leave out the frequency NDBC uses to separate swell from wind sea. Bluegraph calculates it from the swell and wind-sea heights, as the Reference page explains, and, with no wind reading, it counts the wave systems above that frequency as wind sea.