Journal of Geophysical Research–Oceans
Supporting Information for
Spatial and temporal variations of the seasonal sea level cycle in the northwest
Pacific
Xiangbo Feng1,2,3, Michael N. Tsimplis2, Marta Marcos4, Francisco M. Calafat2, Jinhai
Zheng3, Gabriel Jordà4 and Paolo Cipollini2
1. Department of Meteorology, University of Reading, Reading, UK
2. National Oceanography Centre, Southampton, UK
3. State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University,
Nanjing, China
4. IMEDEA (CSIC–UIB), Esporles, Spain
Contents of this file

SODA’s skills in describing the seasonal sea level cycle, including Figures S1-S4

Figures S5-S10
Introduction
This file first provides the assessment of SODA’s skills in describing the seasonal sea
level cycle by comparing against the observations from AVISO and tide gauges. Then,
other supplementary figures that are mentioned in the main text are also provided
behind.
SODA’s skills in describing the seasonal sea level cycle
The mean (1993-2010) and inter-annual variability (1900-2010) of the seasonal sea level
cycle by SODA were estimated and compared with the estimations from sea level
observations (𝜂 − 𝜂𝐼𝐵 ) by AVISO (1993-2013) and tide gauges (1900-2010) respectively.
Note that because SODA does not include the atmospheric pressure loading effect, the
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IB effect (𝜂𝐼𝐵 ) was removed from both AVISO and tide gauge records in this
assessment, ensuring the three datasets are all free of 𝜂𝐼𝐵 .
The mean annual sea level cycle determined by SODA over 1993-2010 is generally in
agreement with the estimations of the seasonal sea level cycle determined by AVISO
over 1993-2013 in most areas, particularly in the open interior and the deep regions of
marginal seas (Figure S1). Compared to observations, SODA underestimates 𝐴𝑎 by 36cm in the shallow waters of the South China Sea, the southwest of the East China Sea
and the south of the Sea of Okhotsk. SODA overestimates 𝐴𝑎 by 2-4cm in the north of
the East China Sea and the Sea of Okhotsk. 𝜙𝑎 determined by SODA is ~2 months
earlier than AVISO estimates in the Sea of Japan, and is advanced by ~1 month in the
coastal regions of the South China Sea and delayed by ~3 months in the coasts of the
Sea of Okhotsk. No significant differences are found in estimations of the semi-annual
cycle parameters when the error bars are taken into account (Figure S2).
The inter-annual variability of 𝐴𝑎 (𝐴𝑠𝑎 ) over 1900-2010 is significantly correlated (pvalue≤0.05 by t-test) between the estimations from tide gauges and SODA (nearby tide
gauges) at 96 (100) of the120 stations (Figure S3 left). The average correlation
coefficient is R=0.59 (0.58) for 𝐴𝑎 (𝐴𝑠𝑎 ). The discrepancies are mainly in the west of the
South China Sea and the north of the East China Sea, where the mean annual cycle is
not well represented by SODA either (Figure S1). SODA over-predicts the temporal
variance of 𝐴𝑎 at 76 stations, and this is indicated by the low values of regression
coefficients (less than 1) for the inter-annual variability between tide gauges and SODA
estimations (Figure S3 upper right), while SODA does well for 𝐴𝑠𝑎 (Figure S3 lower
right).
The regional average of the inter-annual variability over each of six sub-regions fits tide
gauge estimations well, in terms of both the variability and its changing magnitude
(variance) (Figure S4). The correlation coefficient for regional average in each subregion is R=0.53, 0.74, 0.53, 0.57, 0.48 and 0.83 (when heading to north) for 𝐴𝑎 and
R=0.74, 0.68, 0.58, 0.28, 0.72 and 0.40 for 𝐴𝑠𝑎 . Therefore, for the long-term variability of
the seasonal cycle, SODA cannot always well represent its changing magnitudes at
individual tide gauge stations, but it does well when the regional averages are
concerned.
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Figure S1. Mean 𝐴𝑎 (upper) and 𝜙𝑎 (lower) for 𝜂 − 𝜂𝐼𝐵 from AVISO (1993-2013) (left)
and SODA (1993-2010) (middle), and differences of 𝐴𝑎 and 𝜙𝑎 between AVISO and
SODA (right). In left two panels only the annual cycle estimations that pass the
significance test at 95% confidence level are presented, while in the right panel only the
differences where error bars of the two compared values (one from AVISO and the other
from SODA) do not overlap are presented.
Figure S2. Same as Figure S1, but for 𝐴𝑠𝑎 and 𝜙𝑠𝑎 .
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1
0.5
1.5
Correlation
1
Regression
0.5
0
0
1
1.5
0.5
Correlation
1
Scale
0.5
0
0
Figure S3. (upper): Correlation coefficients (left) and regression coefficients (right)
between inter-annual variability of 𝐴𝑎 for 𝜂 − 𝜂𝐼𝐵 obtained from tide gauges and that
obtained from SODA over 1900-2010; (lower), same as (upper), but for 𝐴𝑠𝑎 . Blank
circles indicate the correlations that do not pass the significance test at 95% confidence
level.
Figure S4. (left): Time series of the anomaly of 𝐴𝑎 for 𝜂 − 𝜂𝐼𝐵 observed from tide
gauges (thin grey) and corresponding values determined from SODA (thin red) over
1900-2010, in 6 sub-regions which are specified in Figure 1; (right): same as (left), but
for 𝐴𝑠𝑎 . Bold black and bold red lines are for the regional averages for individual series
determined from tide gauges and SODA respectively in each sub-region.
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cm
10
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no. 120
cm
0
15
10
no. 119
cm
5
15
10
no. 118
5
cm
20
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no. 117
0
cm
20
10
0
1940
no. 116
1950
1960
1970
1980
1990
2000
2010
Figure S5. Time series of 𝐴𝑎 observed at 5 outlier tide gauge records (η) (station
number: 116-120).
Figure S6. (left): Time series of regional average anomaly of 𝐴𝑎 for η observed at tide
gauges (black) and the corresponding regional averages for 𝜂𝐼𝐵 (green) and for 𝜂𝑠𝑡𝑒𝑟
(red) in 6 sub-regions as specified in Figure 1; (right): same as (left), but for 𝐴𝑠𝑎 .
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(a)
(b)
(c)
(d)
Figure S7. (a): Best correlation coefficients of the inter-annual variability of 𝐴𝑎 between
𝜂 − 𝜂𝐼𝐵 , from tide gauges and SODA, and the nearby wind stress; (b): the wind stress
direction (degree) relative to the eastern direction anticlockwise, corresponding to the
wind stress which has the best correlation coefficients with sea level as indicated in (a);
(c) and (d): same as (a) and (b), but for 𝜂 − 𝜂𝐼𝐵 −𝜂𝑠𝑡𝑒𝑟 . Blank circles and areas indicate
the correlations that do not pass the significance test at 95% confidence level.
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(a)
(b)
(c)
(d)
Figure S8. Same as Figure S7, but for best correlations with the sea surface currents.
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Figure S9. Regression coefficients of the inter-annual variability of 𝐴𝑎 between 𝜂 − 𝜂𝐼𝐵
and the sea surface currents at each grid point based on SODA over 1900-2010,
corresponding to the best correlations between the two variables shown in Figure 12a.
Figure S10. Correlation coefficients of the inter-annual variability of 𝐴𝑎 between the wind
stress and the surface currents over 1900-2010 that are used to detect the links with sea
level in Figure 10 and Figure 12. Only the correlations that are significant at 95%
confidence level are plotted.
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