Fróðskaparrit - 01.01.1975, Page 76

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Sca Level Fluctuations in Tórshavn, Preliminary Results
X(k) = I • cos (2 • tt • f^•k•At + «p^) + (8)
with known values for ci5 f; and <pr Nine harmonics were
used with frequencies usually found in tidal series. The known
values for amplitude, frequency and phase are listed in columns
1 and 2 of table II. rk was a generated random series — white
noise — which in this case had a power of 9. The series had a
length corresponding to 112 days of quarter hourly sampling.
After construction the timeseries was digitized to integer values
to compare as closely as possible to the actual sea level series.
The series was then split modulo 4 and one of the parts was
analyzed by the methods described. The MEM spectrum of this
testdata is shown in fig. 1. The nine harmonics are clearly
distinguishable on the figure and the values of frequency and
amplitude determined by analysis are listed in columns 3 and
4 of table II to be compared to the previous two columns.
Results
Harmonic constants The sea level data were analyzed by the
methods listed in the previous part. Fig. 2 shows the MEM
spectrum in the total Nyquist range while figs. 3 and 4 show
parts of it enlarged. It was necessary to split the series modulo
12. for each of the resulting 12 series f';, c ; and cp{ were deter-
mined for the distinguishable peaks. 28 harmonic constituents
were found unambiguously and for each of these the 12 sepa-
rate estimates (or less when unanalysable) were used to find
mean values and standard deviations of frequency, amplitude
and phase. The results are listed in table III. The split series
had a sampling interval of 3 hours, which caused some of the
peaks to be »aliased« (ref. 11). The »corrected« frequencies of
these peaks are listed in the table.
According to Doodson the astronomical tide H at any given
time t may be written (neglecting nodal modulation)
H(t) = Z H^* cos(V^(t) - g^) = r H^•cos(2•n *fQÍ• t + Vqí - Ej.) (9)
where the V . ’s are linear combinations of six astronomical ele-