Specifications

43
5.6 Data processing
Independent of the type of sensor, the DWR-MkIII and DWR-G generate raw north, west and
vertical displacements at a rate of 1.28 Hz. The WR-SG however generates vertical
displacements at 2.56 Hz. Displacements refer to excursions from the average position and
should not be mistaken for position changes relative to the previous position. The raw data is
stored on the logger flash card and output through the radio link. However, the buoy also
outputs processed data through the radio link or via communication satellite. Processed data are
much more compact, nevertheless they still give a good impression of the sea state. Especially
for the limited data transmission capacity of satellites, the processing and compressing is
essential. The processing method is the topic of this section.
In oceanography the use of Fourier spectra of the vertical displacements to represent the
wave conditions is wide-spread. The power spectral density PSD thus obtained quickly shows
what wave amplitudes occur at what frequencies. The first part of this section is devoted to this
straightforward Fourier spectrum calculation and applies to all Waveriders. In the second part
we will deal with a more sophisticated Fourier analysis that also incorporates the horizontal
motion. Now also information on wave ellipticity, wave direction, direction spread, etc.
becomes available. This part only applies to Directional Waveriders (DWR-MkIII, DWR-G).
5.6.1 Wave height spectrum
In the directional buoys (DWR-MkIII, DWR-G), the internal wave spectrum is calculated as
follows. At a sampling rate of fs = 1.28 Hz, every 200 seconds a total number of N=256 heave
samples hk are collected
hk = h(kDt), k=0..N-1 (5.6.1)
where Dt=1/fs is the sampling time. A fast Fourier-transform (FFT) is applied to obtain a
spectrum in the frequency range 0 to fs/2 = 0.64 Hz, having a resolution of fs/N = 0.005 Hz.
In the WR-SG, the sample rate is 2.56 Hz, twice that of the directional buoys. To be able to use
the same spectral routines, only the even displacements are used in the spectrum computation.
Aliasing is avoided by applying a low-pass filter to the data. With this in mind, Eq.(5.6.1) is
also valid for WR-SG data.
The FFT yields Fouriercoefficients according to:
∑
−
=
−=Δ===
1
0
10/)/2exp()(
N
k
lkkll
NltNlfNklihwfHH K π (5.6.2)
with i = √(−1). The w
k
indicate the window coefficients. Datawell applies a cosine-shaped
window over the first and last 32 samples, according to
310
32
cos1
2
1
255
K=
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
⎟
⎠
⎞
⎜
⎝
⎛
−==
−
k
k
ww
kk
π
(5.6.3a)
1=
k
w otherwise (5.6.3b)
For normalization all window coefficients must be divided by
∑
−
=
=
1
0
2
N
k
ksnorm
wfw (5.6.4)