GUIDE WAVE ANALYSIS AND FORECASTING - WMO

Presentation of data and wave climate
statistics
9.3.1 Plot of the data
Having obtained a data set of wave parameters over, say,
a year, it is important to plot the results to obtain an
overall view of the range of values, the presence of any
gaps in the data and any outliers suggesting errors in the
data, etc. Figure 9.1 shows an example, in the form of a
“comb” plot, which provides a good visual impact.
9.3.2 Plotting statistical distributions of
individual parameters
Estimates from the data set of the parameter’s probability
distribution can be obtained by plotting a histogram.
Given, for example, T – z measurements for a year (2 920
values if a recording interval of three hours is used),
then a count of the number of measurements T – z in, say,
0.5-s bins (i.e. 0.0–0.5 s, 0.5–1.0 s, ...) is made and
estimates of the probability of a value in each bin is
obtained by dividing the total in the bin by 2 920. Such
a plot, as shown in Figure 9.2, is called a histogram.
The bin size can, of course, be varied to suit the range
of data — one giving a plot covering 5–15 bins is probably
most informative. Note that a histogram or comb
plot of the spectral peak period, Tp, may give additional
information to a T – z plot. Over large expanses of the
world’s oceans long swells commonly coincide with
shorter wind seas, leading to wave spectra which are
bimodal (double-peaked form). Over a long measurement
series the histogram distribution may also be
bimodal.
Wave height data may also be presented in a
histogram, but it is more usual to give an estimate of the
cumulative probability distribution, i.e. the probability
that the wave height from a randomly chosen member of
the data set will be less than some specified height.
Figure 9.2 —
Histogram of
zeroupcrossing
period measurements
(12 520
valid observations,
including
six calms), at
three-hour
intervals at
OWS “Lima”,
December 1975
to November
1981 (from
HMSO, 1985)
Percentage occurrence
WAVE CLIMATE STATISTICS 103
Estimates are obtained by adding the bin totals for
increasingly high values and dividing these totals by the
number of data values. Sometimes, to emphasize the
occurrence of high waves, the probability of waves
greater than the specified height is plotted — see
Figure 9.3.
9.3.3 Plotting the joint distribution of height
and period
A particularly useful way of presenting wave climate
data, combining both height and period data in one
figure, is an estimate from the data of the joint distribution
of Hs and T – z (often called the joint frequency table
or scatter table). Data are counted into bins specified by
height and period and the totals divided by the grand
total of the data to give an estimate of the probability of
occurrence. In practice — see for example Figure 9.4 —
the estimates are usually multiplied by 1 000, thus
expressing the probability in parts per thousand (‰), and
rounded to the nearest whole number, but with a special
notation to indicate the bins with so few values that they
would be lost by rounding.
It is sometimes more convenient for further analysis
to plot the actual bin totals. In any case, the grand total
should be given with the scatter plot together with the
number of calms recorded. It is also useful to draw on
the scatter plot lines of equal significant steepness
(2πHs/gT – z 2 — see Section 1.3.5). The line representing a
significant steepness of one-tenth is particularly useful,
since this seems in practice to be about the maximum
value found in measurements from open waters. Any
records indicating steeper waves should therefore be
checked for possible errors.
9.3.4 Checks on the data sets
As mentioned above, the various plots of the data and
the estimates from the data of probability distributions