Non-linear Sea Level Variations in the South China Sea from Satellite
Altimetry and Tide Gauges
Yanguang Fu
1,2,*
, Xinghua Zhou
1,2
, Weikang Sun
1
, Dongxu Zhou
2
and Jie Li
2
1
College of Geodesy and Geomatics, Shandong University of Science and Technology, Qingdao, 266590, China
2
First Institute of Oceanography, State Oceanic Administration, Qingdao, 266061, China
Email: ygfu@fio.org.cn
Keywords: Non-linear sea level variation, the South China Sea, satellite altimetry, tide gauge, sea level anomaly
Abstract: Non-linear sea level trend in the South China Sea (SCS) was investigated by means of satellite altimetry and
tide gauge data over 24 years period from 1993 to 2016. GIA corrections and inverted barometer corrections
were applied to the satellite and tide gauge data, and the monthly sea level anomalies (MSLAs) were
compared between each other in details. Thirty tide gauges located in the SCS are in good agreement with
satellite-derived results, with RMSDs ranging between 0.85 and 9.92 cm and correlation coefficients were
more than 0.70 for 85.71% of stations. Non-linear sea level trend of observations during period of 1993-
2016 was analysed by empirical mode decomposition, the sea level rise rate derived from satellite altimetry
and tide gauge data are 4.29 ± 0.29 and 3.93 ± 0.12 mm/year, respectively.
1 INTRODUCTION
Sea level rise due to climate change can generate
significant impact on the social economy, natural
environment and ecosystem, especially in coastal
areas. Many contributing factors make the sea level
trend an integral measure of climate change (Church
et al., 2010; Milne et al., 2009)
Satellite altimetry is an essential tool to describe
the sea-level changes of the open ocean and
marginal seas, as it provides precise and continuous
datasets with global coverage and moderate
spatiotemporal resolution (Cazenave and Llovel,
2010). Nowadays more than 20 years of satellite
altimetry data are available, while most of the
regional sea level changes observed from both
satellite altimetry and tide gauge data were found to
be different (Ishii and Kimotom 2009; Levitus et al.,
2009; Lombard et al., 2005a; Lombard et al., 2005b;
Stammer et al., 2013). However, temporal and
spatial variability of sea level complicates estimation
of sea level rise rates at regional and global scales.
Regional sea level changes may differ substantially
from a global average, showing complex spatial
patterns, which result from ocean dynamical
processes, lateral mass transport fluxes (Pinardi et
al., 2014), and changes in gravity (Stocker et al.,
2013).
South China Sea (SCS) is the largest marginal
sea in Southeast Asia. Due to the unique bottom
topography characteristics and the potential impacts
of sea-level rise in SCS, understanding sea-level
changes and monitoring of sea-level variability in
this area becomes urgent. In the literature, many
works study the sea-level trend in SCS using merged
satellite data (Cheng and Qi, 2007; Feng et al.,
2012). However, the short record of altimetry-based
studies mostly reflects the interannual-decadal
variability and cannot obtain the non-linear sea level
variations. Gridded altimetry data were also
validated at sea-level trend by comparison with tide
gauge data (Luu et al., 2015; Marcos et al., 2015;
Tay et al., 2016). Despite gridded satellite data is an
interpolation of along-track data, it has a better
temporal and spatial resolution due to multi-mission
satellite-based. Therefore, the multi-mission satellite
altimetry gridded data-set were used to analysis the
sea level trend that are not possible with along-track
data.
In this work we analysis the sea-level variations
and trends using the gridded satellite data and all the
tide gauge data available in the SCS over 24 years
period from 1993 to 2016. The objectives of this
paper are, to compare the sea-level anomalies
between satellite data and tide gauge data, in terms
of the error difference and correlation coefficient,
and then to determine the non-linear sea-level
Fu, Y., Zhou, X., Sun, W., Zhou, D. and Li, J.
Non-linear Sea Level Variations in the South China Sea from Satellite Altimetry and Tide Gauges.
In Proceedings of the International Workshop on Environment and Geoscience (IWEG 2018), pages 561-565
ISBN: 978-989-758-342-1
Copyright © 2018 by SCITEPRESS Science and Technology Publications, Lda. All rights reserved
561
variations and residual trend by performing
empirical mode decomposition.
2 DATASETS
2.1 Satellite Altimetry Data
The delayed-time and reference gridded Sea Level
Anomaly (SLA) weekly data product is used
because it is more precise than near-real time data
and has the best possible spatial and temporal
sampling. The SLA observations produced by
SSALTO/DUACS and distributed by AVISO for 24-
year period from January 1993 to December 2016.
The satellite altimetry dataset used consist of
merged data from multi-mission altimeter. Along
track sea-level data are corrected for instrumental
noise, orbit error, tidal effects and the dynamic
atmospheric correction. The correction of
atmospheric pressure and wind forcing was applied
combines the high frequency sea-level variability of
the barotropic ocean model MOG2D with the low
frequency of the inverted barometer (IB) correction
(Carrère and Lyard, 2003; Pascual et al., 2009). The
corrected sea level data were then interpolated with
objective analyses (Ducet et al., 2000), producing a
regular grid with a horizontal resolution of 1/4°,
every seven days. Data were averaged monthly at
each grid point in order to use the same temporal
resolution as the in-situ data.
2.2 Tide Gauge Data
Monthly mean sea level data were downloaded and
extracted from the Permanent Service for Mean Sea
Level (PSMSL). PSMSL provided the Revised
Local Reference (RLR) tide gauge records with
datum control (Woodworth and Player, 2003), in
general, only RLR data should be used for time
series analysis (www.psmsl.org). In the SCS area we
selected 30 stations that have at least 20 years of
data time series from 1993 (the beginning time of
satellite window), a distance up to around 30 km
between station and the nearest grid point, and at
least 90% of the complete valid observations.
Vertical Land Motion (VLM) can affect the local
sea level measurements, in order to obtain the
reliable sea-level rates purely associated with the
ocean dynamics, the VLM corrections have to be
eliminated. System d’ Observation du Niveau des
Eaux Littorales (SONEL) aims at providing high-
quality continuous measurements of sea and land
levels at the coast from tide gauges (relative sea
levels) and from modern geodetic techniques
(vertical land motion and absolute sea levels) for
studies on long-term sea level trends. However, not
all the tide gauge stations co-equipped with the GPS
measurements around the world. In the SCS, though
there are 8 stations listed to measure the land
displacements, their GPS data either have short
(ranging from 4-7 years) records (6 out of 8 stations)
or too much (20.53% and 30.04%, respectively)
missing data (2 out of 8 stations). Since the Glacial
Isostatic Adjustment (GIA) is the major component
of the VLM in addition to the tectonics, subsidence,
sedimentation and self-attraction and loading
(Santamaría-Gómez et al., 2017), the GIA model
result is applied as the VLM correction to the tide
gauge stations.
3 METHODOLOGY
3.1 IB Corrections
In order to compare satellite and tide gauge monthly
sea level data, the IB correction was applied to the
tide gauge data, as explained for the satellite data.
The IB correction was computed using Mean Sea
Level Pressure (MSLP) from the monthly
NECP/NCAR reanalysis data (Kalnay et al., 1996)
provided by National Oceanic and Atmospheric
Administration (NOAA) with a spatial resolution of
2.5°×2.5°. The IB correction mentioned above can
be represented as (Dorandeu and Traon, 1999):
1
(, ,) [ (, ,) ()]
IB
ref
x
yt Pxyt P t
g
η
ρ
=−
(1)
Where
ρ
is the sea water density, P is the
MSLP, and
()
ref
Pt
is the MSLP spatial mean over
the global ocean computed from 1993 to 2016.
3.2 EMD Method
EMD is widely used in dealing with non-linear and
non-stationary time series. EMD decomposes an
oscillatory signal, the time series y(t), with a sifting
algorithm consisting of the following steps:
1. Identify all extrema of y(t).
2. Determine the two envelopes e
max
(t) and e
min
(t)
by spline interpolating the minima and maxima of
the signal.
3. Compute the average of the two envelopes,
R(t)=(e
max
(t)+e
min
(t))/2.
4. Extract the residual signal, d
n
(t)=y(t)-R(t).
IWEG 2018 - International Workshop on Environment and Geoscience
562
5. If d
n
(t) is an IMF, stop. Otherwise, iterate on
d
n
(t) through steps 1 to 4.
Through the EMD process, the time series y(t)
can be decomposed into n IMFs which embody the
local characteristic information of the original signal.
The objective of EMD is to extract IMFs that are
physically and mathematically representative of the
original time series. The decomposition can be
expressed as follows:
1
() () ()
n
i
i
yt x t rt
=
=+
(2)
where the final r(t) is the residual component,
also can be considered as the n+1 IMF, and x
i
(t) is
the finite number of IMFs.
4 RESULTS AND DISCUSS
4.1 Comparison of Satellite Altimetry
and Tide Gauge Data
In this section we compare the sea-level signals of
satellite and tide gauge at tide gauge stations using
the nearest satellite altimetry grid point.
To obtain high precision of SLAs series, quality
analysis was performed at each tide gauge station.
Smoothed and interpolated data were obtained
mainly for the missing data and appreciable errors
using non-linear interpolation method. Figure 1
shows the comparison results between satellite and
tide gauge, the difference errors between them were
ranging from -45.46 to 59.14 cm, the errors have a
normal distribution and 87.35% of them are within
the range of ±10 cm.
The SLAs obtained from both two datasets show
that they present similar performance in most of the
cases considered, with mean root-mean-square
difference (RMSD) was 2.72 cm, and 85.71% of
them were under 5 cm. There are just 3 stations with
higher RMSD than 6 cm. The stations with high
RMSD are mainly due to the SLAs extracted from
satellite and tide gauge have much larger mean
square error difference errors, for example, the mean
square error of satellite and tide gauge in HONNGU
station is 2.88 and 8.74 cm, respectively. These
results clearly indicate that the SLAs obtained from
tide gauge data can be well represented by the
majority of the nearest satellite point data, this is in
agreement with findings by (Ruiz et al., 2015) for
the annual component of sea level variations
compared with the 478 worldwide distributed tide
gauges. Through the correlation analysis of the two
datasets, correlation coefficient of them for 85.71%
of stations was above 0.70, and only two stations
were below 0.50.
Figure 1: Comparison between sea-level signals of
satellite and tide gauge data (left panel). Histogram of
residuals between satellite and tide gauge data (right
panel).
4.2 Sea Level Variations Analysis
Empirical Mode Decomposition (EMD) method is
suitable for the analysis of non-linear and non-
stationary signal sequences with high signal-to-noise
ratio (Barnhart, 2011; Huang et al., 1998). Empirical
mode decomposition is a key to this method, it can
make the complex signal decomposed into a finite
number of Intrinsic Mode Function (IMF), the
decomposition of each IMF component contains the
original signals of the local characteristics of
different time scales.
Figure 2: EMD analysis performed using satellite
altimetry data (blue lines) and tide gauge data (red
lines). The sea-level data time series are
decomposed into 7 IMFs.
To examine the non-linear sea-level variations of
satellite and tide gauges, we calculate the average of
all tide-gauge stations and satellite altimetry sea-
level signals. Considering 24 years of monthly data
in 30 stations, EMD gives 7 IMFs in both data-sets.
Non-linear Sea Level Variations in the South China Sea from Satellite Altimetry and Tide Gauges
563
Significant correlations were found for all the modes,
which increase up to 0.98 in the residual component
(IMF 7). Figure 2 shows the IMFs series, and the
residual component (bottom panel). According to
(Ezer and Corlett, 2012), which explaining that the
residual component can reveal the sea level trend
when EMD was applied to sea-level data, the
residual component in this study shows the sea-level
signals have a positive trend of 4.29 ± 0.29 and 3.93
± 0.12 mm/year in terms of satellite and tide gauge
data.
5 SUMMARY AND
CONCLUSIONS
The aim of this work was to analysis the non-linear
sea-level trends of the SCS retrieved from tide gauge
and gridded altimetry data over 24-year (from 1993
to 2016). The comparison results between 30 tide
gauge stations and the nearest grid satellite point
show error difference are within the range of ±10 cm
for 87.35% of the cases, correlation coefficient was
above 0.70 in 85.71% of stations, and the mean
RMSD was 2.72 cm. By averaging tide gauge and
nearest grid point satellite data in the tide-gauge
stations, two different non-linear sea-level trends
were observed by applying a least squares method to
the residual signals given by EMD from 1993 to
2016, which were 4.29 ± 0.29 and 3.93 ± 0.12
mm/year, respectively.
ACKNOWLEDGEMENTS
The authors would like to acknowledge the AVISO
for providing the gridded satellite altimetry data,
PSMSL for providing the tide gauge data, NOAA
for providing the IB correction data. We are grateful
to the national natural science foundation youth fund
(Grant No. 41706115, 41806214) and national key
research and development program of China (Grant
No. 2016YFB0501703, 2016YFB0501700) for
funding this work.
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