How are spectral wave data derived from buoy motion measurements?

NDBC-reported wave measurements are not directly measured by sensors on board the buoys. Instead, the accelerometers or inclinometers on board the buoys measure the heave acceleration or the vertical displacement of the buoy hull during the wave acquisition time. A Fast Fourier Transform (FFT) is applied to the data by the processor on board the buoy to transform the data from the temporal domain into the frequency domain. Note that the raw acceleration or displacement measurements are not transmitted shore-side. Response amplitude operator (RAO) processing is then performed on the transformed data to account for both hull and electronic noise. It is from this transformation that non-directional spectral wave measurements (i.e., wave energies with their associated frequencies) are derived. Along with the spectral energies, measurements such as significant wave height (WVHGT), average wave period (AVGPD), and dominant period (DOMPD) are also derived from the transformation.

Note that the wave measurements contained in the SeaBreeze CD-ROM only include calculations of WVHGT, AVGPD, and DOMPD. To receive spectral wave energy density data, see the Web page about obtaining archived data.

• For a more detailed explanation on FFT's, see:
  Brigham, E.O., 1988: The Fast Fourier Transform and its Applications. Prentiss Hall International, 448 pp.

• For a detailed description on the applications of Fast Fourier Transforms to wave data, see:
  Tucker, M.J., 1991: Waves in Ocean Engineering: Measurement, Analysis, and Interpretation. Ellis Horwood, LTD., 431 pp.

• For more information about NDBC's wave measuring systems, refer to:
  Steele, K.E. and T.R. Mettlach, 1993: NDBC wave data - current and planned. Ocean Wave Measurement and Analysis - Proceedings of the Second International Symposium. ASCE, 198-207.

NDBC also reports directional wave data for selected stations. Besides buoy heave acceleration, measurements of hull azimuth, pitch, and roll are also necessary for directional waves. Three methods exist for the measurement of hull azimuth, pitch, and roll.

• The first method includes the use of a Datawell Hippy sensor to measure vertical heave acceleration along with pitch and roll. A second sensor, a triaxial magnetometer, is used to measure hull azimuth. For a more detailed description, refer to:

  Steele, K.E., Teng, C-C., and D. W-C. Wang, 1992: Wave direction measurements using pitch and roll buoys. Ocean Engineering, 19, 4, pp. 349-375.

• The second method (no longer used) uses only the triaxial magnetometer to measure hull azimuth, pitch, and roll. Vertical heave acceleration is measured by an accelerometer. For more information, refer to:

  Steele, K.E. and M. Earle, 1991: Directional ocean wave spectra using buoy azimuth, pitch, and roll derived from magnetic field components. IEEE Journal of Ocean Engineering, 16, 4, pp. 427-433.

• The third method uses three orthogonal angular rate measurements to measure hull pitch and roll. Vertical heave acceleration is measured by an accelerometer, and a triaxial magnetometer is used to measure hull azimuth. For more information, refer to:

  Steele, K.E., D.W. Wang, M.D. Earle, E.D. Michelena, R.J. Dagnall, 1998: Buoy pitch and roll computed using three angular rate sensor, Coastal Engineering, 35, Issues 1-2, October 1998, pp. 123-139.

The processing stream as applied to raw, directional measurements is similar to that presented above for non-directional data: RAO's are applied to the acceleration data after all Fourier processing is performed. The main difference between directional and the non-directional wave data is that, for directional data, four frequency-dependent parameters are calculated along with the spectral measurements, WVHGT, AVGPD, and DOMPD. These other parameters are ALPHA1 (mean wave direction), ALPHA2 (principle wave direction), and R1 and R2 (parameters which describe the directional spreading about the main direction).

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