Specifications

59
This transformation has an additional parameter b. For very large values of b (b → ∞) the
transformation becomes linear, r / r
max
≈ i / i
max
. For small values of b, it becomes exponential, r
≈ r
max
exp(-i
max
/ b) exp(i / b). The resolution of the r values is found to be:
brrerrrrr
i
b
iii
/)1(
1
/1
11
+≈−⋅+=−=Δ
+
(5.7.24)
which means that there is an absolute accuracy of r
1
and a relative accuracy of 1/b.
Example: Let r be a wave height in cm. If we want an accuracy of 1 cm and 1%, then we have r
1
= 1 and b = 100. If we have a byte for the integer i (i.e. i
max
= 254), then r
max
= 1162.137 cm. If i
= 255, then r > r
max
(or NaN, not a number).
In Table 5.7.17, the parameters for the transformation are found. Figure 5.7.2 illustrates the
transformation for T
z
and √m
0.
Table 5.7.17. Transformation parameters for the various
oceanographic variables used in the messages.
Variable r
max
i
max
b
ε
abs
ε
rel
i(NaN)
T
z
, and other periods 20 s 254 100 0.02 s 1% 255
√m
0
, and other heights 8.5 m 254 64 2.5 mm 1.5% 255
S, relative power spectral density 1 255 48 10
-4
2% -
1/Q
p
, Goda’s peakedness parameter 1 254 48 10
-4
2% 255
Spr, the directional spread 78.25° 14 8 2.2° 13% 15
Figure 5.7.2. Example of the transformation of real numbers to integers.
5.7.2.9 Smart decimation
Starting point for the “smart decimation” is the averaged spectrum of 128 bins with frequency
spacing of 0.005 Hz, based on 8 consecutive spectra of 256 samples each, see section 5.6. From
these original bins (index k = 5…116), only 27 (index l = 0…26) can be included in the
Compressed heave spectrum message (MsgID = 3). The decimation of bins is made dependent
of the bin (index k
max
) that has the maximal power density, S
max
. Near k
max
more bins are
selected than far from k
max
. Around the spectral peak the frequency steps are small, in the tails
of the spectrum the steps become larger. In this way, the shape of the spectrum, and its
moments, can be reconstructed reasonably from the selection.