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

, Dongxu Zhou

and Jie Li

College of Geodesy and Geomatics, Shandong University of Science and Technology, Qingdao, 266590, China

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

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):

(, ,) [ (, ,) ()]

ref

yt Pxyt P t

=− −

(1)

Where

is the sea water density, P is the

MSLP, and

()

ref

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

(t)=y(t)-R(t).

IWEG 2018 - International Workshop on Environment and Geoscience

562

5. If d

(t) is an IMF, stop. Otherwise, iterate on

(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:

() () ()

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

(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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