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Full text: Reassessment of long-period constituents for tidal predictions along the German North Sea coast and its tidally influenced rivers

A. Boesch and S. Müller-Navarra: Reassessment of long-period constituents for tidal predictions 
1372 
Ocean Sei., 15,1363-1379,2019 
www.ocean-sci.net/15/1363/2019/ 
-60 -40 -20 0 20 40 60 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 
Observation - prediction [min] Observation - prediction [m] 
Figure 7. Histograms of the residuals for tide gauge Cuxhaven and 
year 2016. The different colours indicate predictions based on the 
different sets of partial tides (red: predictions with 43 partial tides; 
yellow: predictions with 39 partial tides), (a) Time differences with 
a bin width of 4 min. (b) Height differences with a bin width of 
0.04 m. 
Table 5. Residuals of predicted and observed times of high and low 
water: mean and standard deviation a in minutes. 
Gauge 
number 
Gauge 
name 
43 partial tides 
39 partial tides 
ß 
O 
ß 
O 
101P 
Borkum 
-2.7 
11.2 
-2.1 
11.0 
103P 
Bremerhaven 
-6.4 
10.4 
-4.6 
10.1 
111P 
Norderney 
1.5 
10.9 
0.7 
10.6 
502P 
Bremen 
-7.3 
10.8 
-5.5 
10.5 
505P 
Büsum 
3.4 
17.5 
4.6 
17.4 
506P 
Cuxhaven 
-0.1 
9.6 
1.0 
9.0 
507P 
Emden 
-9.2 
13.8 
-8.2 
13.3 
508P 
Hamburg 
-10.1 
10.4 
-7.7 
10.3 
509A 
Helgoland 
-2.4 
7.8 
-2.6 
7.7 
51 OP 
Husum 
-5.1 
12.0 
-4.3 
11.7 
512P 
Wilhelmshaven 
-3.2 
10.0 
-2.7 
9.6 
Table 6. Residuals of predicted and observed heights of high and 
low water: mean and standard deviation a in metres. 
ing frequencies. The residuals are the differences between 
the observed and the predicted vertices (times and heights of 
high and low waters) with the same assigned transit number 
and event index k. 
Figure 7 shows histograms of the residuals for the tide 
gauge Cuxhaven. The panels on the left and on the right dis 
play histograms for the times and heights, respectively. Each 
panel contains one histogram for the tidal prediction with 43 
partial tides (red) and one histogram for the tidal prediction 
with 39 partial tides (yellow). Using the new set of partial 
tides, the standard deviation of the residuals decreases from 
9.6 to 9.0 min for the times and from 0.28 to 0.27 m for the 
heights. 
In the same way as for Cuxhaven, residuals are calculated 
for the data of all 98 tide gauges included in the verifica 
tion. The mean values, /i, and standard deviations, er, of the 
residuals for 11 major ports are summarized in Table 5 for 
the times and in Table 6 for the heights. Based on the re 
sults from all tide gauges, the average standard deviation of 
the residuals is 13.2 min or 0.28 m, respectively, using the set 
of 39 tidal constituents. In most cases, the new set of partial 
tides gives small improvements in /i and a. 
The percentage changes. Act, in the standard deviations 
are presented in the histograms in Fig. 8 (times) and Fig. 9 
(heights) for all 98 tide gauges. The percentage change is 
calculated in the following way: 
Act [%] = 100 % • g39 pi ~ g43 pi , (6) 
043 p.t. 
where <739 pt . and <743 pt . are the standard deviations of the 
residuals using the predictions with 39 partial tides (p.t.) and 
43 partial tides, respectively. The average reductions of the 
standard deviations are 2.41 % (times) and 2.30% (heights). 
The two tide gauges with the largest improvements in this 
Gauge 
number 
Gauge 
name 
43 partial tides 
39 partial tides 
ß 
O 
ß 
O 
101P 
Borkum 
0.05 
0.24 
0.03 
0.24 
103P 
Bremerhaven 
0.06 
0.28 
0.04 
0.28 
111P 
Norderney 
0.03 
0.25 
-0.01 
0.24 
502P 
Bremen 
0.01 
0.27 
-0.01 
0.26 
505P 
Büsum 
0.04 
0.29 
0.01 
0.28 
506P 
Cuxhaven 
0.05 
0.28 
0.04 
0.27 
507P 
Emden 
-0.01 
0.28 
-0.02 
0.27 
508P 
Hamburg 
-0.08 
0.33 
-0.12 
0.31 
509A 
Helgoland 
0.03 
0.25 
0.02 
0.24 
510P 
Husum 
0.02 
0.29 
0.00 
0.28 
512P 
Wilhelmshaven 
0.05 
0.27 
0.03 
0.27 
study, both with regard to times and heights, are Holmer Siel 
(BSH gauge number 649B) at the North Frisian coast and 
Bremervörde (687P) in the river Oste. Further tide gauges 
with improved standard deviations are located all around the 
area of investigation. Regarding the times (Fig. 8), the four 
tide gauges with increased standard deviations are Wester 
land (620P) and Hörnum (624P), located on the North Frisian 
island of Sylt, and Dove-Elbe (727P) and Bunthaus (729P), 
located upstream of the river Elbe. Regarding the heights 
(Fig. 9), the five tide gauges with the largest positive changes 
are also located upstream in the Elbe, namely Geesthacht 
(732D), Altengamme (732A), Zollenspieker (73IP), Ilmenau 
(730A) and Fahrenholz (730C). The water levels in this part 
of the Elbe are partly influenced by river discharge, which 
can lead to deviations from the tidal predictions. 
The change in constituents has an influence on the remain 
ing periodicities in the residuals. Periodograms are calcu 
lated for the two sets of residuals (times and heights) for 
each tide gauge. The 98 periodograms of each type are aver-
	        
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