A. Boesch and S. Müller-Navarra: Reassessment of long-period constituents for tidal predictions 
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Ocean Sei., 15,1363-1379, 2019 
Table 4. The modified and adopted new list of long-period partial 
tides. The rank R indicates the importance of a partial tide for tidal 
analysis, based on the combined evaluation of data from all tide 
gauges. 
Doodson 
£U (° tn 1 ) 
Description, name 
R 
ZZZZAZ 
0.0548098 
lunar nodal precession 
6 
ZZZBZZ 
0.2306165 
half lunar apsidal precession 
13 
ZZAZZZ 
1.0201944 
tropical year, Sa 
7 
ZZBXZZ 
1.8097724 
31 
ZZBZZZ 
2.0403886 
half tropical year, Ssa 
17 
ZAXZZZ 
11.5978420 
14 
ZAXAZZ 
11.7131503 
MSm 
8 
ZAYXZZ 
12.3874200 
34 
ZAYZZZ 
12.6180365 
19 
ZAYAAZ 
12.7881545 
39 
ZAZYZZ 
13.5229227 
anomalistic month, Mm 
3 
ZAZZZZ 
13.6382309 
tropical month 
4 
ZAZZAZ 
13.6930407 
38 
ZAZAZZ 
13.7535391 
21 
ZABBAZ 
15.9640460 
36 
ZBWZZZ 
24.2158785 
11 
ZBXZYZ 
25.1812631 
35 
ZBXZZZ 
25.2360729 
half synodic month, MSf 
1 
ZBYZZZ 
26.2562673 
12 
ZBZXZZ 
27.0458453 
33 
ZBZYZZ 
27.1611535 
15 
ZBZZZZ 
27.2764618 
half tropical month, Mf 
2 
ZBZZAZ 
27.3312716 
27 
ZCVAZZ 
36.9492232 
Sv2 
10 
ZCXYZZ 
38.7589956 
SN 
16 
ZCXZZZ 
38.8743038 
24 
ZCXAZZ 
38.9896120 
MStm 
22 
ZCZYZZ 
40.7993844 
Mfm 
23 
ZDUZZZ 
49.4519514 
29 
ZDVZZZ 
50.4721458 
fourth synodic month, 2SM 
5 
ZDXZZZ 
52.5125347 
MSqm 
9 
ZDXZAZ 
52.5673444 
37 
71)7777. 
54.5529235 
30 
ZF.TAZZ 
62.1852961 
25 
ZEVYZZ 
63.9950685 
2SMN 
28 
ZEVAZZ 
64.2256849 
26 
ZFTZZZ 
75.7082187 
sixth synodic month 
20 
ZFVZZZ 
77.7486076 
18 
ZHRZZZ 
100.9442917 
eighth synodic month 
32 
7 9 11 16 21 29 34 
Figure 6. The partial tides (identified by their rank R from Ta 
ble 4) that can be resolved as a function of the (minimum) length of 
the time series. If two partial tides cannot be resolved against each 
other, the one with the lower rank is dropped. Note the logarithmic 
time axis from 0.2 to 20 years. The numbers at the top are the counts 
of partial tides. 
new set are compared with observations. The predictions are 
made for the year 2016 and are compared with tide gauge 
observations from the same year. 
5.1 Tidal analysis and prediction 
We calculate tidal predictions (times and heights of high and 
low waters) with the HRoI using (i) the 43 partial tides from 
Set 2 in Table 2 and (ii) the 39 partial tides derived from our 
analysis. The data and software are otherwise identical. The 
predictions are based on amplitudes a„, (see Eq. 1) that are 
determined from a tidal analysis of water level records from 
1995 to 2013 (19 years). Data are only used from tide gauges 
that have delivered enough observations in this time period to 
include all partial tides in the analysis. Additionally, the tide 
gauges must have delivered observations for the year 2016. 
The 98 tide gauges that fulfil these criteria are marked in the 
column “Used for verif.” in Table Al. All tide gauge data are 
prepared as described in Sect. 4.1, including the removal of 
extreme events from the observations that are used for com 
parison. The analysis is applied in two iterations with a 3er 
clipping in-between. 
5.2 Evaluation of residuals 
In this section, we present results from the analysis of the 
residuals in the following order: the distributions of resid 
uals for the tide gauge Cuxhaven, the means and standard 
deviations for some major ports, the changes in the standard 
deviations for all tide gauges, and the changes in the remain-