Deriving offshore tidal datums using satellite altimetry around Malaysian seas

Abstract

Tidal datums are important for calculating spatial coordinates especially the elevation relative to mean sea level and also crucial for defining the state sovereignty boundaries over maritime areas. Normally, sea level was measured by tide gauges along the coastal for tidal datums computation. However, knowledge of tides is still restricted in coastal areas. Furthermore, tidal range at offshore was simply assumed to be similar as coastal due to the difficulties installing offshore tide gauges. The launching of satellite altimeter technologies with precise orbit determination since 1993 had provided significant accuracy of sea surface height (SSH) measurements. The observed SSH from satellite altimetry can be offered as tide gauge measurements at each location globally. This study aims to derive offshore tidal datums using satellite altimetry around Malaysian seas. SSH time series from TOPEX, Jason-1, Jason-2 and Geosat Follow On (GFO) were analysed using harmonic analysis approach to estimate harmonic constants. A minimum of 19 years tidal predictions were then performed using UTide software to determine Lowest Astronomical Tide (LAT) and Highest Astronomical Tide (HAT). These tidal datums were interpolated into regular 0.125° grids and were assessed with ten selected coastal tide gauges. The findings showed the Root Mean Square Error (RMSE) of spline interpolation yielded better accuracy, 25.5 cm (LAT MSL ) and 17.4 cm (HAT MSL ) as compared to the RMSE of Kriging interpolation, 31.8 cm (LAT MSL ) and 33.8 cm (HAT MSL ). In conclusion, deriving offshore tidal datums can serve as input data to unify marine database with coastal areas and also can support many marine applications.

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STACLIM 2021
IOP Conf. Series: Earth and Environmental Science 880 (2021) 012011
IOP Publishing
doi:10.1088/1755-1315/880/1/012011
1
Deriving offshore tidal datums using satellite altimetry
around Malaysian seas
M H Hamden1*, A H M Din1,2 D D Wijaya3 and M F Pa’suya4
1 Geospatial Imaging and Information Research Group (GI2RG), Faculty of Built
Environment and Surveying, Universiti Teknologi Malaysia, 81310 Johor Bahru,
Johor, Malaysia
2 Geoscience and Digital Earth Centre (INSTEG), Faculty of Built Environment and
Surveying, Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor, Malaysia
3 Geodesy Research Division, Faculty of Earth Science and Technology, Institute of
Technology Bandung, Jl. Ganesha 10, Bandung, Indonesia
4 Environment and Climate Change Research Group, Faculty of Architecture,
Planning & Surveying, Universiti Teknologi MARA, Perlis Branch, Arau Campus,
02600 Arau, Perlis, Malaysia
*Corresponding E-mail: mhanif87@live.utm.my; amihassan@utm.my
Abstract. Tidal datums are important for calculating spatial coordinates especially the
elevation relative to mean sea level and also crucial for defining the state sovereignty
boundaries over maritime areas. Normally, sea level was measured by tide gauges along the
coastal for tidal datums computation. However, knowledge of tides is still restricted in coastal
areas. Furthermore, tidal range at offshore was simply assumed to be similar as coastal due to
the difficulties installing offshore tide gauges. The launching of satellite altimeter technologies
with precise orbit determination since 1993 had provided significant accuracy of sea surface
height (SSH) measurements. The observed SSH from satellite altimetry can be offered as tide
gauge measurements at each location globally. This study aims to derive offshore tidal datums
using satellite altimetry around Malaysian seas. SSH time series from TOPEX, Jason-1, Jason-
2 and Geosat Follow On (GFO) were analysed using harmonic analysis approach to estimate
harmonic constants. A minimum of 19 years tidal predictions were then performed using
UTide software to determine Lowest Astronomical Tide (LAT) and Highest Astronomical
Tide (HAT). These tidal datums were interpolated into regular 0.125° grids and were assessed
with ten selected coastal tide gauges. The findings showed the Root Mean Square Error
(RMSE) of spline interpolation yielded better accuracy, 25.5 cm (LATMSL) and 17.4 cm
(HATMSL) as compared to the RMSE of Kriging interpolation, 31.8 cm (LATMSL) and 33.8 cm
(HATMSL). In conclusion, deriving offshore tidal datums can serve as input data to unify
marine database with coastal areas and also can support many marine applications.
Keywords: Tidal datums, Offshore, satellite altimetry, Lowest Astronomical Tide, Highest
Astronomical Tide
Track Name: Coastal Management and Marine Ecosystem

STACLIM 2021
IOP Conf. Series: Earth and Environmental Science 880 (2021) 012011
IOP Publishing
doi:10.1088/1755-1315/880/1/012011
2
1. Introduction
Tides are usually defined as the vertical periodic rise and fall of water on the surface of the earth that
occurs twice in a little more than a day. According to [1], tides are also described as the periodic
variation in the level surface of the ocean, inlets, bays, gulfs and estuaries resulting from the
gravitational forces of the moon and the sun. Scientists have worked for the past two centuries to
headway scientific knowledge of ocean tides [2]. The process of measuring tides is known as tidal
observation by using an equipment called tide gauge station. Statistically averaging sea level
measurements is the process of stabilising a fluctuating surface to serve as tidal datum [3]. There are
many ways to average sea level which giving rise to a variety of tidal datums. Tidal datums are
defined as a standard reference elevation used from which to reckon heights or depths in terms of a
certain phase of the tide [4, 5, 6]. They are predominantly used to measure depth or water level as well
as critical in defining spatial coordinates such as latitude, longitude and elevation with respect to Mean
Sea Level (MSL). Not only that, they are also important as legal bodies for establishing the state
sovereignty over maritime boundaries.
In determining the tidal datums, tides generally measured by tide gauges along the continental
coastline which refer to coastal tide gauges. Although the long-term sea level observations can
enhance the understanding of tides, the knowledge is still constrained in the vicinity of coastal areas.
[2] stated that the tide measurements further away from coastal made by bottom pressure gauges is
slow and less effective. In Malaysia, Department of Survey and Mapping Malaysia (DSMM) is the
authority responsible for acquiring, processing, archiving and disseminating the long-term tidal data
[7]. At present, there are eleven tide gauge stations along the Peninsular Malaysia coast (West
Malaysia) and eight tide gauge stations along the coast of Sabah and Sarawak (East Coast). However,
less discoverable on offshore tidal datums in this region is due to the difficulties installing the offshore
tide gauges. There might be few offshore tide gauges being installed which could only restricted with
the used by the offshore companies. In the past, the tidal range at the coastal was simply inferred to be
similar to offshore and the tide phase was computed using shallow water wave theory [8].
Credit goes to an active remote sensing technique so called satellite altimetry, launched in 1970s
that provided a comprehensive technique in measuring the global ocean. Satellite altimetry has been
used by certain researchers to investigate ocean activities in the specific regions. For instance, [9]
analyze the SSH from TOPEX series satellites of 19-year time series to extract the tidal harmonic
constants in the Brazilian coast. It shows the Root Sum Square misfit (RSSmisfit) values are less than
12 cm in deep ocean. Besides, [2] has developed an empirical ocean tide models namely OSU12
models by utilizing an enhanced multi-mission satellite altimetry data from TOPEX, Jason-1/-2,
Envisat and GFO based on a novel method via spatio-temporal combination, together with a robust
estimation technique. The study shows substantial improvement which apparently in regions with high
hydrodynamic variability. In Malaysia, [10] has studied on the derivation of tidal constituents from
satellite altimetry for coastal vulnerability assessment. It used Mean Tidal Range parameter derived
from tidal models where the tidal models were generated from TOPEX and Jason-1 data. The used of
tidal models are projected to supplement the existing coastal management system in order to scrutinize
the severity of coastal damages caused by sea level rise impacts, particularly in Malaysian coastal
areas. Furthermore, Yahaya et al. [11] and Zulkifle et al. [12] have developed regional mean sea
surface (MSS) models for Malaysian seas using multi-mission satellite altimetry data. This study
generated MSS model by merging 11 years of repeated SSH observations from several satellite
altimeter missions.
The improvement of precise orbit determination technique, instrumental and geophysical
corrections have provided better accuracy of sea surface height (SSH) measurements since the launch
of TOPEX/Poseidon mission [13]. The obtained SSH from satellite altimetry revisits at the similar
point for each orbit cycle can be offered as tide gauge measurements at each location globally.
Therefore, this study is an attempt to derive offshore tidal datums using satellite altimetry around
Malaysian seas. SSH time series of TOPEX class (TOPEX, Jason-1 and Jason-2) and GFO missions
were analysed using harmonic analysis approach to estimate the amplitude and phase of eight selected

STACLIM 2021
IOP Conf. Series: Earth and Environmental Science 880 (2021) 012011
IOP Publishing
doi:10.1088/1755-1315/880/1/012011
3
harmonic constants namely M2, S2, K1, O1, N2, K2, P1, Q1, MF, MM, SA and SSA. These harmonic
constants were then used for tidal prediction of at least 19 years to determine the tidal datums. The
tidal datums referred in this study are Lowest Astronomical Tide (LAT) and Highest Astronomical
Tide (HAT) relative to MSL. Section 2 describes the materials and method, followed by results and
discussion in section 3. Lastly, section 4 concludes the overall study.
2. Materials and method
2.1 Study Area and Datasets
Along track SSH from TOPEX class and GFO missions were extracted using Radar Altimeter
Database System (RADS). The extracted SSH data spanning over 23 years for joint TOPEX class and
8 years for GFO mission as listed in table 1. TOPEX, Jason-1 and Jason-2 missions are denoted as
TOPEX class because these missions are moving on the same orbit track. The study area was bounded
within the geographical coordinates of 0° N - 9° N in latitude and 98° E - 121° E in longitude. Figure 1
illustrates the study area limited to the specified coordinates as well as the along track TOPEX class
mission (blue) and GFO mission (green). The black triangles indicate the coastal DSMM tide gauge
stations used to assess the estimated offshore tidal datum. Meanwhile, the red points are randomly
selected for visualization of SSH time series.
Table 1. List of satellite altimetry data used.
Satellite Mission
Phase
Cycle
Period Time
TOPEX
A
001-364
January 1993 – August 2002
Jason-1
A
001-260
January 2002 – January 2009
Jason-2
A
001-303
July 2008 – October 2016
GFO
A
037-223
January 2000 – September 2008
Figure 1. Along-track altimetry missions of TOPEX class (blue) and GFO (green) within the study
area as well as the distribution of selected coastal DSMM tide gauge (black triangle).
2.2 Satellite Altimetry Processing and Formation of SSH Time Series
As aforementioned, all satellite altimetry used in this study were extracted using RADS server in
Universiti Teknologi Malaysia (UTM), providing the latest information on orbits and geophysical
corrections. The computation of SSH were processed by applying the preferred range and geophysical
correction in the Malaysian region, removing the invalid data and also generating the corresponding
refined corrections. SSH altimetry can be derived by using the equation (1) [10,14,15].

STACLIM 2021
IOP Conf. Series: Earth and Environmental Science 880 (2021) 012011
IOP Publishing
doi:10.1088/1755-1315/880/1/012011
4
) (1)
Where, is the corrected sea surface height, is the satellite altitude, is the altimeter
range measurement, is the dry tropospheric correction, is the wet tropospheric correction,
is the ionospheric correction, is the sea state bias correction, is the solid earth tide
correction, is the pole tide correction, is the ocean tide correction, is the dynamic
atmospheric correction and is the other errors induced in altimetry measurement. However, it is
noted that was excluded from being applied into the equation. This is to prevent the ocean tide
signal to be eliminated as this signal is crucial in estimating harmonic constants.
2.2.1 Formation of SSH Time Series
This is done by extraction of SSH at each cycle of discrete points. Ground tracks of altimetry with
repeated orbit missions generally do not coincide accurately with each other. Thus, collinear analysis
is utilised to compute each SSH point of collinear tracks similar to the reference track. In this study,
the collinear track of first cycle was treated as the reference track. Thus, from the reference track and
corresponding collinear track, the formation SSH time series can be plotted as shown in figure 2.
Figure 2. Schematic diagram on formation of SSH time series.
2.2.2 Tidal Aliasing.
TOPEX class and GFO missions have different repeated periods which are 9.9156 days and 17.0505
days, respectively. Thus, both missions suffer from tidal aliasing effect due to altimeter’s long
temporal sampling. According to Shannon sampling theorem, in order to completely rebuild the
original signal, it must be sampled at least twice of the frequency, . For instance, , where
is the Nyquist frequency. A signal with period can be completely rebuild if the samples are
obtained at interval of less than . If not, the signal of are aliased to a longer period to , which
is aliased period [2,16]. The aliasing period can be computed by using the equation (2) [17].
(2)
Where, is the frequency of tidal component, is the period sample and the bracket [.] in the
formula of [ ] is the fix function that return greatest integer less than argument. The
information of actual period and aliased period from TOPEX class and GFO missions are tabulated in
Table 2. The aliased period obtained from both missions are calculated by using equation (2). The
consequence of the aliasing effect on tide signals detected from altimetry mission is that the length of
each tidal constituent appears to be longer than its actual period. The aliasing period of each
constituent is used in harmonic analysis to estimate amplitude and phase as well as for tidal prediction.

STACLIM 2021
IOP Conf. Series: Earth and Environmental Science 880 (2021) 012011
IOP Publishing
doi:10.1088/1755-1315/880/1/012011
5
Table 2. Actual and Aliased Tidal Period for TOPEX class (9.9156 days) and GFO (17.0505 days).
Tidal
Constituents
Actual Period
(cph)
Actual Period
(cpd)
TOPEX Aliased Period
(cpd)
GFO Aliased
Period (cpd)
M2
12.42
0.52
62.11
317.11
S2
12.00
0.50
58.74
168.82
K1
23.93
1.00
173.19
175.45
O1
25.82
1.08
45.71
112.95
N2
12.66
0.53
49.53
52.07
K2
11.97
0.50
86.60
87.72
P1
24.07
1.00
88.89
4467.14
Q1
26.87
1.12
69.36
74.05
MF
327.86
13.66
36.17
68.71
MM
661.31
27.55
27.55
44.73
SSA
4382.92
182.62
182.62
182.62
SA
8765.74
365.24
365.26
365.26
Notes: cph = cycle per hour, cpd = cycle per day
2.3 Tidal Analysis and Prediction
Harmonic analysis approach was adopted for tidal analysis and prediction in this study. This analysis
is performed using MATLAB package ‘Unified Tidal analysis and prediction’ or UTide, developed by
[18]. Based on [18], the UTide was built on the foundation of T_TIDE by [19], integrating concepts
from [20] and [21]. SSH time series from TOPEX and GFO missions were analysed to estimate the
selected tidal harmonic constants at each point of along-track. Then, these estimated tidal harmonic
constants (amplitudes and phase lags) were put into tidal harmonic prediction equation in order to
predict the tides. A tidal prediction can be computed by summing up the oscillating contributions of
some number of tidal constituents. The formula for tidal analysis and prediction used in this study are
expressed in the equation (3) [16, 18, 22].
(3)
Where, is the sea level for predefined time ( at discrete location . is the
mean sea level of analysed data and represents the total number of tidal constituents used; ,
and represent the amplitude, frequency and delay phase of th tidal constituents, respectively;
is the astronomical argument, while and are nodal factor and nodal phase, respectively. Based on
[23], LAT and HAT can be computed over a minimum of 19 years using harmonic constants estimated
from at least 19 years of tidal data or other method known to produce reliable results. However,
according to [24], using 19 years of tidal prediction to compute LAT and HAT are always reasonable.
Thus, in this study, the tides were predicted for at least 19 years to determine the tidal datums.
2.4 Tidal Interpolation Method
The generation of tidal datums surfaces in this study involves two interpolation method namely
Ordinary Kriging (OK) and a minimum curvature (MCr) technique called (regularised) spline. Both
methods were used to interpolate the along-track altimetry data into a regular grid of 0.125°. Both
were assessed to determine the best interpolation method for generation of tidal datums surfaces.
Assessment was performed by comparing the interpolated points with the selected coastal tide gauges.
2.4.1 Ordinary Kriging

STACLIM 2021
IOP Conf. Series: Earth and Environmental Science 880 (2021) 012011
IOP Publishing
doi:10.1088/1755-1315/880/1/012011
6
Kriging is a geostatistical interpolation method which is based on statistical models inclusive of
autocorrelation. This method fits a mathematical function to specific points or all points within the
specific radius to determine the output value of predicted locations. The formula is expressed in
equation (4) [25, 26].
(4)
Where, is the measured value at the th location; is an unknown weight for the measured
value at the th location; is a predicted value and is the total number of measured values.
2.4.2 Minimum Curvature Spline
This method is widely used in the earth sciences. The interpolated surface is equivalent to a thin,
linearly elastic plate moving through each data with the minimum amount of bending [20]. The
formula for spline interpolation is expressed in equation (5) [27, 28].
(5)
Where, is the number of points, is the coefficient found by the solution of linear equations and
is the distance between point and point. Since this study applied the regularised option,
and were expressed in the equation (6) and (7).
(6)
Where, are the coefficient found by the solution of linear equations.
(7)
Where, is the distance between the point and sample, is the weight parameter, is the
modified Bessel function and is the constant equal to 0.577215.
2.5 Statistical Data Assessment
The Root Mean Square Error (RMSE) is used to measure the quality of the results where it computes
the difference between the predicted values and the true values. In this study, there are two statistical
data assessment were performed. First, the RMSE was calculated to determine the reliability of the
predicted SSH derived from satellite altimetry by comparing with the observed SSH. Second
assessment was performed by calculating the RMSE values between the interpolated points from two
interpolation techniques and the selected coastal tide gauges which can be expressed in equation (8).
(8)
Where, is the predicted values (i.e., interpolated points), is the true value which is the coastal
tide gauges, and is the total number of samples. However, for the first assessment, is indicated as
predicted SSH values while is the observed SSH values.
3. Results and Discussion
3.1. Time Series Modelling and Residuals
SSH time series of TOPEX class and GFO missions were modelled by applying the equation (3).
These time series were predicted at each point of along-track altimetry as illustrated in figure 1. Each
point from the along-track of predicted SSH time series were randomly selected (labelled as red dots

STACLIM 2021
IOP Conf. Series: Earth and Environmental Science 880 (2021) 012011
IOP Publishing
doi:10.1088/1755-1315/880/1/012011
7
in figure 1) at each Malaysian sea’s regions namely the Malacca Straits, the South China Sea, the Sulu
Sea, and the Celebes Sea. This is to visualise the modelled time series. It is noted that the point must
be selected at the offshore area. Figure 3 shows the selected SSH modelled time series and its residuals
from TOPEX class on the left column well as GFO mission on the right column. The observed and
predicted SSH time series are plotted in blue and green lines, respectively. Meanwhile, the red plotted
lines indicate as the residuals of SSH time series. These residuals were calculated by computing the
differences between the predicted and observed SSH time series. Subsequently, the quality of the
predicted SSH can be determined based on these residuals by using RMSE computation. It can be seen
that the SSH time series data from TOPEX class is denser than GFO mission. This is because the
repeated period of TOPEX class is shorter than GFO which is 9.9156 days and 17.0505 days,
respectively. The highest RMSE value between observed and predicted SSH from TOPEX is at
Malacca Straits which recorded 10.1cm, followed by Celebes Sea (9.8 cm), Sulu Sea (7.6 cm) and
South China Sea (7.3 cm). This might be due that Malacca Straits is a closed sea area which the tidal
characteristics would most likely have a large gradient. Nevertheless, the highest RMSE value from
GFO mission is at Celebes Sea which recorded 10.9 cm, followed by Malacca Straits (7.9 cm), Sulu
Sea (7.0 cm) and South China Sea (6.5 cm). Therefore, it can be inferred that the precision of tidal
prediction from both missions were reasonable at offshore area since the RMSE is within 10.9 cm to
6.5 cm.

STACLIM 2021
IOP Conf. Series: Earth and Environmental Science 880 (2021) 012011
IOP Publishing
doi:10.1088/1755-1315/880/1/012011
8

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IOP Conf. Series: Earth and Environmental Science 880 (2021) 012011
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doi:10.1088/1755-1315/880/1/012011
9
Figure 3. Observed (blue) and predicted (green) time series and residuals (red) of TOPEX class (left)
and GFO (right) missions according to the areas (Malacca Straits, South China Sea, Sulu Sea and
Celebes Sea).
3.2. LAT and HAT with respect to MSL
LAT and HAT can be defined as the lowest or (highest) water level which can be predicted to occur
under average meteorological conditions as well as any combination of astronomical conditions. Both
may be derived by the analysis of a number of years of tidal data or predictions which is normally 18.6
years to account for the full nodal cycle. In this study, the SSH time series from both missions were
predicted for at least 19 years or more where predicted time series from TOPEX class is between 1993
until 2019. Meanwhile, predicted time series from GFO is between 2000 until 2019. The lowest and
highest predicted tide indicate the LAT and HAT, respectively. Later, the derived LAT and HAT from
satellite altimetry were interpolated and validated against the selected coastal DSMM tide gauges as
distributed in Figure 1. Before the results could be compared with the tide gauges, the derived data
need to be converted with respect to MSL. The computation of LAT and HAT with respect to MSL
was depicted in Figure 4.
Figure 4. Computation diagram of LAT and HAT are relative to MSL.
Along-track satellite derived tidal datums from TOPEX class and GFO missions had to be merged
together before being interpolated into a regular grid. Crossover offset was applied to the along-track

STACLIM 2021
IOP Conf. Series: Earth and Environmental Science 880 (2021) 012011
IOP Publishing
doi:10.1088/1755-1315/880/1/012011
10
GFO mission to a TOPEX reference surface in order to minimise the orbital track errors and the
discrepancy of satellite’s orbit frame between two missions. The combination of TOPEX class and
GFO along-track missions (LATMSL and HATMSL) were then interpolated into a regular grid of 0.125°
by using ordinary kriging and minimum curvature spline method as shown in Figure 5. Based on
Figure 5, it can be seen that the middle of the Malacca Straits has the greatest tidal range of LATMSL
and HATMSL compared to other regions which recorded up to -2.6 m and 3.0 m, respectively. The tidal
range of LATMSL and HATMSL in the middle of South China Sea, Sulu Sea, and Celebes Sea show the
values within -0.9 m to -1.1 m (LATMSL) and the values within 0.9 m to 1.2 m (HATMSL). The greatest
tidal range of LATMSL and HATMSL also can be seen at the southwest of East Malaysia in the South
China Sea which recorded up to -2.1 m and 2.2 m, proportionately. Meanwhile, at the north-western
part of South China Sea, near to the Gulf of Thailand depicted the lowest tidal range of LATMSL and
HATMSL which recorded the values near to zero meter. Apparently, the tidal ranges are mostly larger
near to the coastal areas compared to the offshore areas. It is visible at the coastal part of Celebes Sea
as shown in Figure 5. The reason is due to the satellite altimetry data acquired near the coastlines are
contaminated by the inclusion of land in the footprint signal or by the fact that the tide is on the ebb
[2]. Moreover, the tidal datum models using ordinary kriging method generated smoother contour
lines as compared to minimum curvature spline method. However, these gridded offshore tidal datum
models were validated with the selected coastal tide gauges in order to identify the best interpolation
method.
Figure 5. LATMSL and HATMSL models using ordinary kriging (Top) and minimum curvature spline
(Bottom).
3.3. Statistical Assessment of Tidal Models
Generally, the best way to validate these offshore tidal datums are by comparing them with the
offshore tide gauges. However, lack of deployment offshore tide gauges as well as difficulty in
obtaining the offshore tidal data from the offshore authorities had hindered this validation method.
Thus, this study adopted the statistical assessment of offshore tidal datums by validating the satellite

STACLIM 2021
IOP Conf. Series: Earth and Environmental Science 880 (2021) 012011
IOP Publishing
doi:10.1088/1755-1315/880/1/012011
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altimetry derived offshore tidal datums models with ten selected DSMM tide gauges. The results of
the assessment were described in Table 3 (LATMSL) and Table 4 (HATMSL).
Table 3. Statistical results between satellite derived offshore LATMSL (ordinary kriging and minimum
curvature) and in situ tide gauge data (Units in meter).
Tide
Gauge
Station
In Situ
Ordinary
Kriging
Minimum
Curvature
Ordinary
Kriging – In
Situ
Minimum
Curvature – In
Situ
1
P. Langkawi
-1.781
-1.758
-1.516
0.023
0.265
2
P. Pinang
-1.662
-1.117
-1.330
0.545
0.332
3
Lumut
-1.800
-1.293
-1.425
0.507
0.375
4
Tg. Sedili
-1.684
-1.389
-1.428
0.295
0.256
5
P. Tioman
-1.894
-1.584
-1.529
0.310
0.366
6
Cendering
-1.395
-1.210
-1.219
0.185
0.176
7
Geting
-0.717
-0.724
-0.919
-0.007
-0.202
8
Miri
-1.135
-1.212
-1.274
-0.077
-0.139
9
Bintulu
-1.389
-1.689
-1.528
-0.300
-0.139
10
K. Kinabalu
-1.223
-0.843
-1.089
0.380
0.134
Mean
0.186
0.142
STD
0.258
0.211
RMSE
0.318
0.255
Table 4. Statistical results between satellite derived offshore HATMSL (ordinary kriging and minimum
curvature) and in situ tide gauge data (Units in meter).
Tide
Gauge
Station
In Situ
Ordinary
Kriging
Minimum
Curvature
Ordinary
Kriging – In
Situ
Minimum
Curvature – In
Situ
1
P. Langkawi
1.751
1.915
1.482
0.164
-0.269
2
P. Pinang
1.391
1.508
1.413
0.117
0.022
3
Lumut
1.578
1.449
1.458
-0.129
-0.120
4
Tg. Sedili
1.429
1.045
1.189
-0.384
-0.240
5
P. Tioman
1.762
1.609
1.559
-0.153
-0.203
6
Cendering
1.527
1.472
1.429
-0.055
-0.098
7
Geting
1.012
1.020
1.027
0.008
0.015
8
Miri
1.182
1.180
1.173
-0.002
-0.009
9
Bintulu
0.977
1.901
1.298
0.924
0.321
10
K. Kinabalu
1.213
0.974
1.141
-0.240
-0.072
Mean
0.025
-0.065
STD
0.337
0.161
RMSE
0.338
0.174
For offshore tidal datum of LATMSL, the RMSE values obtained between the minimum curvature
spline model and in situ data is smaller than the ordinary kriging model which recorded 25.5 cm and
31.8 cm, respectively. Meanwhile, the RMSE values of HATMSL between minimum curvature spline

STACLIM 2021
IOP Conf. Series: Earth and Environmental Science 880 (2021) 012011
IOP Publishing
doi:10.1088/1755-1315/880/1/012011
12
and in situ data is also smaller than the ordinary kriging model which yielded 17.4 cm and 33.8 cm,
respectively. Thus, it can be inferred that the offshore tidal datums models generated using minimum
curvature spline method has better agreement with coastal tide gauges compared to ordinary kriging
models despite ordinary kriging produced smooth contour surfaces.
4. Conclusion
This paper generally studies on deriving the offshore tidal datums using SSH satellite altimetry data
from TOPEX class and GFO missions around Malaysian seas bounded to the latitude of 0° N - 9° N
and longitude of 98° E - 121° E. SSH time series of both missions were analysed by adopting
harmonic analysis approach to estimate the selected tidal constituents. The estimated tidal constituents
were then used to predict the tides at each of along-track altimetry time series points. The outcomes
from this study illuminated that the predicted and observed tides at offshore areas have good precision
which yielded the RMSE values within 6.5 cm to 10.9 cm. The models of LATMSL and HATMSL were
generated by using two different interpolation methods namely ordinary kriging and minimum
curvature (regularised) spline and were assessed with selected coastal tide gauges. The results showed
the models (LATMSL and HATMSL) adopting regularised spline method have the smallest RMSE values
which indicates the best interpolation method. Therefore, it can be concluded that the regularised
spline method is the best interpolation method in this study to predict the offshore tidal datum
compared to the ordinary kriging method.
In conclusion, this study indirectly can create an awareness towards Malaysian hydrographic
society especially regarding the importance of satellite altimetry in supporting hydrographic survey
practice. The encouraging results from this study are capable in establishing seamless vertical datum
by integrating the tidal datums between coastal and offshore area. Other than that, deriving tidal datum
is necessary to support in the establishment of marine boundaries as well as the requirement for
conducting shoreline mapping.
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Acknowledgments
Highly acknowledged to the TU Delft, Altimetric LLC for providing the satellite altimetry data
through Radar Altimeter Database System (RADS). Appreciation to the Department of Survey and
Mapping Malaysia (DSMM) for providing coastal tide gauge data. This research is funded by the
Ministry of Higher Education (MOHE) under the Fundamental Research Grant Scheme (FRGS) Fund,
Reference Code: FRGS/1/2020/WAB05/UTM/02/1 (UTM Vote Number: R.J130000.7852.5F374).