The Stability of Tide Gauges in the South Pacific Determined from Multiepoch Geodetic Levelling, 1992 to 2010

Abstract

Tide gauge data is important for determining global or local sea level rise with respect to a global geocentric reference frame. Data from repeated precise levelling connections between the tide gauges and a series of coastal and inland benchmarks, including Continuous GPS (CGPS) benchmarks, are used to determine the stability of tide gauges at 12 locations in the South Pacific. The method for determining this stability is based on a constant velocity model which minimises the net movement amongst a set of datum benchmarks surveyed since the installation of the tide gauges. When assessed at a 95% confidence interval, and with the exception of the Solomon Islands, none of the tide gauges were found to be in motion relative to their CGPS benchmarks. The Solomon Islands estimate is considered to be unreliable since the CGPS benchmark was recently established and has been surveyed fewer than three times. In Tonga and Cook Islands, the tide gauges were found to be disturbed or affected by survey errors whereas the Vanuatu results were affected by earthquakes.

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The stability of tide gauges in the South Pacific
determined from multi-epoch geodetic levelling, 1992
to 2010
Manoj Nilesh Deo a , Ramesh Govind b & Ahmed El-Mowafy c
a Department of Spatial Science, Curtin University, GPO Box U1987, Perth, Western
Australia, 6845
b Minerals and Natural Hazards Division, Geoscience Australia, GPO Box 378, Canberra, ACT
2601, Australia
c Curtin University, GPO Box U1987, Perth, Western Australia, 6845 Phone: +61 2 6293 2420
Fax: +61 2 6293 2420
Accepted author version posted online: 25 Mar 2013.
To cite this article: Manoj Nilesh Deo , Ramesh Govind & Ahmed El-Mowafy (2013): The stability of tide gauges in the South
Pacific determined from multi-epoch geodetic levelling, 1992 to 2010, Marine Geodesy, DOI:10.1080/01490419.2013.786003
To link to this article: http://dx.doi.org/10.1080/01490419.2013.786003
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The stability of tide gauges in the South Pacific determined from multi-epoch geodetic
levelling, 1992 to 2010
Manoj Nilesh Deo1, Ramesh Govind2, Ahmed El-Mowafy3
1PhD Candidate, Department of Spatial Science, Curtin University, GPO Box U1987, Perth,
Western Australia 6845
2Minerals and Natural Hazards Division, Geoscience Australia, GPO Box 378, Canberra, ACT
2601, Australia
3 Senior Lecturer, Curtin University, GPO Box U1987 Perth, Western Australia 6845
Phone: +61 2 6293 2420
Facsimile: +61 2 629 32420
Email: Manoj.Deo01@gmail.com
The stability of tide gauges in the South Pacific determined from multi-epoch geodetic
levelling, 1992 to 2010
Tide gauge data is important for determining global or local sea level rise with respect to
a global geocentric reference frame. Data from repeated precise levelling connections
between the tide gauges and a series of coastal and inland benchmarks, including
Continuous GPS (CGPS) benchmarks, is used to determine the stability of tide gauges at
12 locations in the South Pacific. The method for determining this stability is based on a
constant velocity model which minimises the net movement amongst a set of datum
benchmarks surveyed since the installation of the tide gauges. When assessed at a 95%
confidence interval, and with the exception of the Solomon Islands, none of the tide
gauges were found to be in motion relative to their CGPS benchmarks. The Solomon
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Islands estimate is considered to be unreliable since the CGPS benchmark was recently
established and has been surveyed less than 3 times. In Tonga and Cook Is, the tide
gauges were found to be disturbed or affected by survey errors whereas the Vanuatu
results were affected by earthquakes.
Keywords: precise levelling; vertical velocity; inner constraint adjustment;
deformation monitoring; sea level monitoring
1. Introduction
The South Pacific Regional GPS Network (SPRGN) consists of Continuous Global
Positioning System (CGPS) stations located in 12 Pacific Island countries. The SPRGN was
established under the South Pacific Sea Level and Climate Monitoring Project (SPSLCMP). This
project was funded by AusAID and developed in 1991 as an Australian Government response to
concerns raised by Pacific Island countries over the impact of global warming on climate change
and sea level rising in the Pacific region (Bureau of Meteorology, 2007). The project also
supports the operation of SEAFRAME tide gauges co-located with the CGPS stations within
proximity of a few kilometres. The locations of these sensors are shown in Figure 1. The
installation of the CGPS stations has commenced in 2001, during the five-year third phase of the
project. The installation dates of the tide gauge sensors and the CGPS stations are summarised in
Table 1, with the distance between them along the levelling route.
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Figure 1: The South Pacific Regional GPS Network.
Table 1: Installation dates for the tide gauge sensors and CGPS stations in the South Pacific, with
the distance between them along the levelling route.
The absolute vertical velocity of the CGPS stations is determined from combining long-
term GPS solutions with mm accuracy, in a globally consistent geocentric terrestrial reference
frame such as the International Terrestrial Reference Frame (ITRF) available, for example, from
the ITRF2008 solution (Altamimi et al., 2011). In general, the CGPS monument consists of a 1.5
m concrete pillar with a solid concrete foundation on geologically stable ground, measuring 2 m
x 2 m with a depth of up to 4 m. However, the tide gauges are usually located on wharves, which
are structurally unstable and subject to gradual movements. Thus, continuous monitoring of the
vertical movement of the tide gauges, relative to the CGPS stations, is required at higher
accuracy than the estimates of relative sea level rise. The Tide Gauge Benchmark Monitoring
Pilot Project (TIGA-PP) has identified the importance of high quality ties between the tide gauge
and CGPS stations (Blewitt et al., 2006). For periods earlier than the installation of the CGPS,
the vertical monitoring of tide gauges was undertaken relative to an array of deep driven
benchmarks (BM). These BMs consist of high quality durable steel, driven several metres into
the ground until it reaches bedrock or other stable material. The vertical movement of the tide
gauge is monitored by precise geodetic levelling (1992 to 2005) and thereafter by EDM
trigonometric height traversing using Total stations (Rueger & Brunner, 1981). The levelling
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surveys are repeated at approximately 1.5 year intervals, and each survey takes about a week to
complete. A typical survey involves forward and backward level runs between BMs located
along the levelling route from the tide gauge to the CGPS BM.
Several studies have been done to determine velocities and uplift rates of BMs from
repeated levelling (Makinen and Saaranen, 1998; Makinen et al., 2003; Schlatter et al., 2005;
Lenotre et al., 1999; Verdonck, 2006; Kimata et al., 2004; Murray and Wooller, 2002). Anastasio
et al. (2006) estimated vertical movements of BMs in a complex geodynamic location in Italy. In
these approaches, the height changes were referenced to a single BM, which was considered to
be stable; and the movement of all other marks is determined relative to this BM. The results can
be significantly corrupted if the fundamental BM moves between successive levelling surveys.
This research avoids referencing the movement of all points to a single BM. The least-
squares estimation technique with an inner constrain approach has been used for estimating the
vertical velocities, their uncertainties and the initial heights of BMs over two decades of repeated
levelling data. The method also accounts for local geophysical effects such as earthquakes. In
order to correctly interpret sea level change, the precision of the vertical rate of the tide gauge
should be better than the precision of sea level rise estimates. A recent global estimate for sea
level rise in the past century has been estimated as 1.7 mm  0.2 mm/yr (Church and White,
2011), which has a similar rate to previous values estimated by Tushingham and Peltier (1991),
and Douglas (1997).
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The structure of the paper is as follows. Section 2 describes the method of adjustment
employed in this study, which minimises the net motion of a subset of datum points. Section 3
describes the raw data under consideration and its reduction procedures. Results are presented in
Sections 4, with discussions and conclusions given in Section 5 and 6, respectively.
2. Methodology
Figure 2: Simple levelling array.
Consider an array of coastal and inland deep driven BMs, A, B and C, as illustrated in Figure 2
and assume that each BM is deforming with a constant vertical velocity. The observation
equations for the measured relative height differences,

HBA,

HCB at the initial epoch, t0, and
subsequent epochs, ti, are expressed as follows (Leal, 1989)
         
. .
0 0 0 A
A B i B BA i BA i
H t H t t t H H H t v t
 
      
 
  (1)
         
. .
0 0 0 B
B C i C CB i CB i
H t H t t t H H H t v t
 
      
 
  (2)
where
.
A
H
,
.
B
H
and
.
C
H
are the velocities of points A, B and C and


0
A
H t
,


0
B
H t
and


0
C
H t
are their initial heights;

HBA and

HCB are the relative heights between the points A-B
and B-C, vBA and vCB are small residuals in the observation model, which are assumed Gaussian
white noise. From Equations (1-2), if there are n number of points, there will be (n-1)
observations (differential heights) and 2n unknowns (velocity and initial height for each point).
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A rank deficiency would result in the design matrix for a least-squares solution for the problem
at hand, unless there are at least [2n/(n-1)] epochs of survey data. For the given example, at least
three epochs of data are needed to remove the rank deficiency. Instead of holding the height of
one benchmark fixed, as is the case in the traditional approach, an inner constraint is introduced
to facilitate direct comparison of multi-epoch data on a consistent datum. The constraint imposed
is that the mean height of a set of datum points, as determined in the initial survey, remains
constant for all subsequent epochs, such that for the given example:












0 0 0
A i B i C i A B C
H t H t H t H t H t H t
     (3)
and considering
     
.
0 0
A
A i A i
H t H t t t H
   (4)
)()()( iBAiAiB tHtHtH  (5)
and
)()()()()()( iCBiBAiAiCBiBiC tHtHtHtHtHtH  (6)
Substituting Equations (5) and (6) into (3) results in the following condition equation for each
epoch of survey
.
0 0 0 0
2 ( ) 2 ( ) ( ) ( ) ( ) 3( )
A
A BA i CB i B C i
H t H t H t H t H t t t H
       (7)
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In order to introduce a height datum, the height of one of the datum points, e.g., HA(t0), is
adopted as an approximate value, thus is known. For each epoch of survey, there are n-1
observation equations, one condition equation (Equation 7) and 2n-1 unknowns (since HA(t0) is
known), thus a solution is possible with just two epochs of data. The parameters to be solved
using least-squares will comprise the initial heights of the BMs and their point velocities, given
as:
   
...
0 0
T
A B C
B C
H t H t H H H
 

 
 
x (8)
For the given example, with two epochs of survey (t1 and t2), there are six equations and five
unknowns. The combined observation and condition equations read:
1 0 1 0 1 0
11 0
0 1 1 1 0
2 0 2 0 2 0
2 2 0
2 0
0 2 2
( ) ( ) 1 0 ( ) ( )
( ) 1 1 0 ( )
2 ( ) 2 ( ) ( ) 1 1 3( ) 0
( ) ( ) ( ) ( )
1 0
( ) 1 1 0 ( )
1 1 3( )
2 ( ) 2 ( ) ( )
BA A
CB
A BA CB
BA A
CB
A BA CB
H t H t t t t t
H t t t
H t H t H t t t
H t H t t t t t
H t t t
t t
H t H t H t
     
 
 
 
 
 
     

 
    

 
 
  
   
   
 
 
0
0
1 0 .
.
2 0 .
( )
0
( )
( )
0
0
( )
00
B
C
A
B
C
H t
H t
t t
H
H
t t
H
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
(9)
The variances of these parameters, given in this paper, are adopted from the diagonal of
the inverse normal matrix in the least-squares solution. Initially, the datum points consist of high
quality deep driven benchmarks (i.e., structurally stable), which have been surveyed since the
first epoch, t0. The choice of which BM to take its initial height for this purpose is arbitrary and
will not affect the vertical velocities determined. The estimated heights can be shifted to another
datum value, if required. In addition, during successive levelling, some datum points may be
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destroyed or found to deform significantly relative to other datum points. This requires their
elimination from the datum list. However, it must be ensured that the condition defined by the
inner constraints can be re-established in all subsequent epochs in order to directly compare
results of different epochs. Therefore, the datum points considered for such comparison must be
the same in the initial epoch and during subsequent epochs.
Modelling effects of earthquakes and other discontinuities
If any of the BMs are found to be disturbed by earthquakes, physical impacts or localised
deformations, a height discontinuity is introduced. It is assumed that the velocity remains the
same before and after the event. For example, if a displacement occurred at a non-datum BM (X)
along the levelling run, which lies between the datum points B and C, the observation equation
becomes
         
. .
0 0 0 B X
XB i XB i B X i
H t v t H t H t t t H H
 
       
 
 
e
h (10)
Where he is the height displacement vector between BMs B and X. The displacement vector is
introduced on the date of the event and remains in the observation equations for all subsequent
epochs. A similar equation can be formulated for the observation from X to C, by reversing the
sign of the displacement vector. Equation (3) remains unchanged since the displacement does not
affect the inner constraint condition, i.e., the mean height of the datum points remains
unchanged.
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Observation weighting
The observations were weighted at first order levelling precision, with a standard deviation of 1
mm per k, where k is the levelled distance in km. This level of accuracy was routinely
achieved by both levelling methods, as indicated by the survey closures between the forward and
backward level runs. If the survey misclose exceeds this tolerance, the survey party repeats the
levelling. The standard deviations for the observed quantities on the left hand side of the
condition represented by Equation (7), -2ΔHBA (ti), –ΔHCB(ti), are also determined using first
order levelling standards, based on the distances between datum BMs.
3. Description of the Data Used in this Study
The data used in this study were from levelling surveys conducted in 12 Pacific Island
countries during the period 1992 to 2010. Details of the survey epochs and in-country surveys
are given in Table 2. The fundamental BMs, which were held fixed in previous survey reports,
e.g., from Geoscience Australia (2007), are shown in the last column of the table in bold font. In
total, data from 42 points were included in datum computations. Precise geodetic levelling was
the method of survey between 1992 and 2005, and EDM trigonometric height traversing was
used thereafter. A comparison between height results computed from the two methods during the
period 2004-2006 was undertaken in each country (except the Solomon Islands). The epochs for
which the tide gauges were connected to the CGPS BMs are shown in bold font in the second
column of Table 2. The precise levelling was done using a first order automatic level (Wild NA
3003) with 2 m invar staves. The manufacturer specified precision for this equipment is 0.4
mm/km for a backward and forward run. Considering a maximum levelling distance of 5 km at
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Samoa, the expected levelling error would be 2 mm. This makes it possible to detect the stability
of the tide gauge at 1.5 year intervals to within the precision of current sea level rise estimates of
1.7 mm ± 0.2 mm/yr.
The instruments used for EDM trigonometric height determination were Leica total
stations (TCA1800 and TCA2003) with high quality prisms (GPH1A). The manufacturer
specified angular precision of these equipment are 1” and 0.5” for TCA1800 and TCA2003,
respectively, and 1 mm + 1 ppm for distance measurements. The backsight and foresight
distances are kept equal to within 0.5 m. The standard deviation in the height difference
measured between two points, defined as s

H, is given as (Ceylan and Baykal, 2006)
4
2 2 2 2 2
2
2cos 2sin 4
H D Z k
D
s Z Z R
  
 
     (11)
where Z is the zenith angle, D is the sight distance, R is the mean radius of the Earth (6371km),

D and

Z are the standard deviations of the distance and zenith angle, respectively and

k is the
uncertainty in the difference of the coefficient of refraction between the two points. A sight
distance of 50 m and a slope of 5 degrees are typical in the South Pacific environment. Taking
the uncertainty in the coefficient of refraction as 0.05 for the forward and backward run (ibid.),
the uncertainty in height difference between two consecutive points at 100 m apart is evaluated
as 0.12 mm. Assuming that all instrument setups were independent of each other and applying
the law of propagation of errors, the total uncertainty in 5 km of total levelling distance would be
0.86 mm. Thus tide gauge BM stability determination is also possible using trigonometric
height traversing with a high precision total station.
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Table 2: Details of the levelling surveys in each country. The epochs for which the tide gauges
were connected to the CGPS BMs are shown in bold font in the second column. The
fundamental BMs which were previously held fixed are shown in bold font in the last column.
A typical levelling survey consists of a levelling route commencing at the tide gauge
point and terminating at the CGPS BM. The distance between these two points is given in Table
1. A series of deep driven (stable) BMs were placed along the route, which were levelled to
during traversing. Generally, it is aimed to have one deep driven BM for every kilometre of
levelling. The levelling run is split into a backward and forward run between two consecutive
deep driven bench marks, while keeping the closure errors to within the first order levelling
standards (Geoscience Australia, 2007). Initially, the deep driven BMs that have been surveyed
since the initial epoch were adopted as datum points. Since the duration of each survey is
relatively short (approximately 1 week), it is assumed that no deformation occurred during this
period and the epoch of survey is adopted as the middle of this period.
The precise levelling observations were available to our study from the National Tidal
Centre, Australian Bureau of Meteorology. The trigonometric height traversing observations
were available from the National Geospatial Reference System (NGRS) Project records,
Geoscience Australia. The observations used in this study are the measured height differences
between successive BMs measured at multiple epochs. These height differences have been
corrected for closure errors.
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EDM Trigonometric Height Traversing
Trigonometric height traversing was performed through the use of the leap-frog
approach. The distance measurements were corrected for temperature, pressure and relative
humidity effects. No geometric corrections were applied to the distances to correct for projection
effects and nor was any correction applied for refraction. Refraction errors were almost
eliminated using a standard field procedure of keeping the back and forward sight distances
between the total and the target stations equal. This was ensured by measuring the sight distances
prior to setting up the instrument using a box tape, with an accuracy of 0.1 m. Residual refraction
errors which may remain are highly random and dominated by the gradient of the terrain as well
as distance to the forward and backward targets (Holdahl, 1979). They are practically eliminated
when keeping the sight distances below 100 m (Kharangani, 1987). Since the average gradient of
the terrain in the study areas was quite low (below 5 degrees) and the sight distances to the
forward and backward targets were typically less than 50 m, refraction errors were not corrected
any further.
4. Results
Table 3 shows the initial heights and vertical velocity estimates with their standard deviations
computed from the least-squares adjustment using the proposed method for the fundamental
datum BMs (which were held fixed in previous surveys). The results for the CGPS BM and tide
gauges are also given for all locations . The standard deviations for the initial heights and vertical
velocities were obtained from the variance-covariance matrix of the least-squares solution, The
vertical velocities were statistically not significant at the 95% confidence level in some cases.
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Table 3 also gives the overall Root-Mean-Square (RMS) of the measurements residuals and the
statistical degrees of freedom for each country’s adjustment. The fundamental BMs in Cook Is,
Fiji, Samoa and Solomon Is exhibit significant velocities after applying the inner constraint
adjustment, thus they were erroneously held fixed with zero velocity in previous surveys.
Table 3: Table 3: Initial heights and vertical velocity estimates, with standard deviations of
fundamental datum BMs, CGPS BMs and the tide gauges at the 12 locations in the Pacific
Islands. The statistical significance of the parameters is assessed at the 95% confidence level.
Also given are the RMS of residuals and degrees of freedom for the least-squares adjustment.
To transform the previously determined heights onto a height datum with inner constraint
applied, the velocity of the fundamental BM determined from the inner constraint adjustment
was applied to the heights from previous surveys, where they were held fixed. Figure 3 shows
the difference in tide gauge levels in Fiji using the two methods, as an example. The transformed
heights are computed as
 
.
0
BM
BM i
H t t H  , where HBM is the height of a BM from previous
surveys and .
BM
H is its velocity. Table 4 shows the RMS of the deviations of the transformed
height from the heights obtained by the proposed constant velocity method, for the tide gauges
and CGPS BMs in each country.
The net velocity of the tide gauge relative to the GPS BM and its standard deviation is given in
Table 5 for all the 12 tide gauges. This is calculated by subtracting the velocity of the CGPS BM
from the tide gauge velocity vector. Its standard deviation is determined using the law of
propagation of errors. Another item of interest is the raw offsets between the CGPS BM and the
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tide gauge BM compared to the same offsets after applying the inner constraint adjustment. The
raw offsets are obtained by simply differencing the tide gauge height (HTG) from the CGPS BM
height (HBM) at each epoch
TG BM
H H

, whereas the offset after applying the adjustment is
affected by their relative velocities. The offsets were computed
as
     
. .
0 0 0 TG BM
TG BM i
H t H t t t H H
 
 
   
 
 
 
. These offsets are given in Table 6, Appendix A.
Figure 4 shows the raw offset between the heights of CGPS BMs and the tide gauges for surveys
after installation of the CGPS and the modelled offsets prior to this, together with their standard
deviations. Solomon Is has been excluded since it had high residuals due to insufficient levelling
connections after establishment of the CGPS. A downward trend signifies a sinking tide gauge
with respect to the CGPS BM and the linear component prior to CGPS installation is estimated
from the inner constraint adjustment. Note the high variations in Vanuatu due to earthquake
disturbances, Cook Islands due to survey errors and Tonga due to disturbance to the tide gauge.
Table 4: RMS of deviations of the transformed height from the heights obtained by the proposed
constant velocity method.
Figure 3: Height variations of the tide gauge in Fiji (FIJ13) using the conventional method
holding one height as fixed (blue), the proposed method with inner constraint adjustment (green),
and the conventional results transformed by the velocity difference between the two methods
(pink).
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Figure 4: Change in height differences, with error bars, between the CGPS BM and the tide
gauge BM at all countries, except Solomon Is. A 10 mm offset has been applied between each
dataset to improve visibility.
The absolute velocities of the CGPS stations in a global and consistent reference frame
were obtained by processing GPS data and presenting point coordinates in the ITRF2008
(Altamimi et al., 2011). The velocities, and their standard deviations, were obtained by analysing
the time series of station positions since their establishment. The velocities in ITRF2008 are also
given in Table 5 for all stations except Solomon Is and Marshall Is, which were not in the
solution since they are relatively new. In comparing the velocities from the two determinations,
their difference is statistically not significant, since their difference falls within one standard
deviation of the combined standard deviations of the two determinations.
Table 5: Velocity (mm/yr), with standard deviation of the tide gauges, relative to is associated
CGPS BM, from the proposed method. The ITRF2008 vertical velocity and standard deviation of
the CGPS station, in the last column, are from Altamimi et al. (2011).
5. Discussion of Results
Analysis of results of the CGPS BMs show that with the exception of Solomon Islands, none of
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the tide gauges exhibit significant motion at the 95% confidence level, using the proposed
method. However, the results in Solomon Is are not considered reliable due to the fact that only a
few epochs of levelling have been conducted since the recent establishment of the CGPS station.
Detecting and removing effects of earthquakes and other disturbances
After obtaining the least-squares solution, the RMS of the residuals for each observation or
condition equation were calculated, and their values are given in Table 4. Typically, these were
better than 1 mm at the tide gauge and 1.5 mm at the CGPS BM. Higher values are investigated
further. The results for Cook Is showed a 6 mm residual for point BM18 in 2008, indicating that
the point had moved in that epoch. Thus, a height discontinuity was introduced at this point,
resulting in a displacement of -13.9 mm  1.4 mm and an improvement of the RMS for residuals
to 0.83 mm. Similar movement was found for BM PNG2 in Papua New Guinea, which moved
by -4.90 mm  1.38 mm in 2008.
The initial adjustment for Tonga revealed high residuals of up to 10 mm at the tide gauge,
whereas the RMS for residuals was 1.39 mm. Earlier survey reports stated that BM TON60 had
moved by 7 mm (Geoscience Australia, 2007). Therefore, a height discontinuity was introduced,
which resulted in a displacement of -6.8  3.0 mm. Although the overall RMS of the adjustment
was improved to 1.05 mm, the high RMS residuals did not improve at the tide gauge.
Vanuatu is regularly struck by strong earthquakes and vertical subsidence as high as 117
± 30 mm, which have been recorded for the period 1997 to 2009, followed by an uplift of 200
mm after three major earthquakes of 7 October 2009 (Ballu et al., 2011). The Vanuatu tide gauge
and nearby BMs were clearly affected by the Earthquake of 2 Jan 2002, as indicated by a large
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uncertainty in the estimated velocity vector in the initial adjustment. A height discontinuity was
introduced at VAN2 on the date of the earthquake and a displacement vector was estimated.
After the adjustment, large residuals persisted between the points VAN2–VAN14 and VAN14–
VAN16, therefore height discontinuities were also estimated at these points. After applying the
displacement vectors to the results, the velocity of the tide gauge continued at the same rate
before and after the co-seismic displacement. The total displacement between BMs VAN3 and
the tide gauge at VAN16, was estimated as -34.84 mm  6.20 mm. This displacement must be
considered when analysing tide gauge data. Note that the standard deviation is relatively higher
than the accuracy required for sea level determinations. Although this method reduces the effect
of co-seismic displacement on BM movements, the uncertainty of the parameter estimates
increases with each discontinuity.
Assessment of the Quality of parameters
The quality of the parameters (the initial heights and velocities of BMs), in terms of their
standard deviation, is contained in the variance-covariance matrix after the least-squares
adjustment. Newer BMs were established during the installation of the CGPS stations to satisfy
the condition of the use of one BM per kilometre of levelling. The standard deviations of the
initial height and velocity estimates of these marks are generally poorer than those of the older
ones. In this section, the quality of estimated heights and their velocities of these points are
discussed.
In Cook Islands, the GPS BM had standard deviations of 9.84 mm and 0.77 mm/yr in the
initial height and velocity estimates, respectively. BM34 and BM35 had high standard deviations
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in their initial heights, 5.29 mm and 4.90 mm, and velocity standard deviations of 0.43 and 0.42
mm/yr, respectively. Though these points had fewer epochs of observations than others, they
have been surveyed at least six times since 2001 and their high uncertainties were investigated.
The report for the 2002 survey (National Tidal Facility, 2002b) stated that movements of -3 mm
to -4 mm occurred at BMs BM18, BM26, COO10 and COO56, relative to the fundamental BM,
BM27. All these points are in a localised area, close to the tide gauge, and it was inferred that a
local subsidence had taken place. However, this appears more as an outlier rather than a step
when plotting the time series of the height. Thus, it is more likely that a survey error occurred
between BM27 to BM18 during the 2002 survey, which accumulated as the survey progressed
towards the tide gauge.
Fiji had good overall results with standard deviations in height less than 4 mm and all
velocity standard deviations were less than 0.3 mm/yr. The standard deviations of points with
fewer epochs of observations (BM3246-8 and GPS BM) were slightly higher (3-4 mm; 0.2-0.3
mm/yr) compared to points which have been surveyed since the initial epoch, which on average
were with standard deviations 1-2 mm; 0-0.16 mm/yr. Kiribati had standard deviations better
than 2 mm in height and 0.2 mm/yr in velocity. KIR46-49, which have been surveyed for fewer
epochs, had slightly higher standard deviations (3-4 mm; 0.2-0.3 mm/yr). In PNG, the GPS and
BMs PNG29-31, which were installed much later than the initial epoch, had higher standard
deviations (1-2 mm; 0.1-0.2 mm/yr) than old marks (0.5-0.7 mm; 0.04-0.15 mm/yr).
In Marshall Is, MAR100 and the GPS BM had height standard deviations of 11.35 mm
and 4.86 mm, with velocity standard deviations of 0.51 mm/yr and 1.82 mm/yr, respectively.
Both have been observed for only three epochs since 2007. MAR107, which has been surveyed
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only twice, had high standard deviations of 13.28 mm in height and 1.96 mm/yr in velocity.
Other BMs had height standard deviations between 3mm and 5 mm and velocity standard
deviations between 0.5 mm/yr and 1.5 mm/yr. These exceed the accuracy requirements for
accurate sea level monitoring. However, the uncertainties are expected to improve with more
surveys in future.
In Nauru, the newer BMs, NAU36-38, had higher standard deviations (2.8-4.2 mm; 0.24
– 0.35 mm/yr). The CGPS BM had very high standard deviation of 16.72 mm and 1.26 mm/yr,
whereas other points had low standard deviations (0.7-1.3 mm; 0.1-0.2 mm/yr). It is noted that
the survey distance between the CGPS BM and the nearest deep driven bench mark, NAU16, is
quite large at 2.15 km. It is likely that survey errors between these points have accumulated and
are causing the large uncertainties. Therefore, a deep driven BM between these points is strongly
recommended to satisfy the condition of one BM per kilometre.
In FSM (Pohnpei) the standard deviations of heights and their velocities for all points
were better than 2mm and 0.4 mm/yr for all points except for the GPS BM, which were 2.96 mm
and 0.6 mm/yr. This is likely due to a survey error in the first levelling connection in 2003,
which can be verified by comparing results with those from the future surveys The large standard
deviation could be also due to accumulation of refraction errors, particularly when the slope of
the terrain changes between BM FSM4 (H(t0)=1.7550) and FSM5 (H(t0)=20.5900, with a
distance of 0.96 km) and between FSM5 and CGPS BM (H(t0)=38.0036; with a distance 0.88
km). Figure 5 shows high deviations of the height changes from those using the constant velocity
model, after transforming to the inner constraint datum at the CGPS BM in Pohnpei (FSM).
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Figure 5: Height variations of the CGPS BM in Pohnpei (FSM) with and without the inner
constrain adjustment as well as the height from the constant velocity model.
Samoa had one new BM, BM220, which had high standard deviations (4.68 mm; 0.74 mm/yr)
compared to other BMs (0.84-1.41 mm; 0.15-0.38 mm/yr). The vertical rate of the tide gauge
BM, -0.720.3 mm/yr, is the highest amongst all tide gauges in the project. In Solomon Islands,
the CGPS BM and new BMs, FBM8-9, which had only three epochs of survey had higher
standard deviations (2-8 mm; 0.2-3.5 mm/yr) compared to other stations (0.5-1.2 mm; 0-0.1
mm/yr). The velocity of the CGPS BM is very high at -3.48  0.49 mm/yr, which requires
further investigations using observations from future surveys. There could be an error in one of
the surveys which is causing the large velocity changes. Refraction errors could be affecting the
results, particularly when the slope of the terrain changes between BM FBM9 (H(t0)=4.74900m)
to FBM3 (H(t0)=54.0451m, distance 0.37 km) and FBM3 to CGPS BM (H(t0)=54.3598m;
distance 0.31 km).
Tonga had very high standard deviations for the estimated heights of GPS station and
new BMs, TON60-62, (4-16 mm; 0.4-1.3 mm/yr) compared to old BMs (3-5 mm; 0.2-0.5
mm/yr). These large standard deviations suggest presence of untreated errors in the data or high
disturbance at BMs. In Tuvalu, the GPS station and new BMs, BM25-28, had high standard
deviations (6-19 mm; 0.5-1.15 mm/yr). BM28 had worst results since it has been surveyed only
twice, followed by BM25 which was surveyed three times. Other BMs had relatively better
results (0.9-1.1 mm; 0.1 mm/yr). Vanuatu had results of a good quality (1.7-3.4 mm; 0.2-1
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mm/yr). However, the standard deviations of the height and velocity of the tide gauge exceeded
the accuracy requirements for accurate sea level monitoring.
Detecting stability of datum benchmarks
The velocities of the datum BMs relative to each other were considered to determine their
stability. Unstable BMs were detected by outlier analysis based on student t-distribution, where a
velocity, is an outlier if its deviation from the mean, which should be very close to zero, divided
by its standard deviation exceeds a 95% confidence level of statistical significance
In FSM (Pohnpei), BM FSM3 was removed from the datum points and the adjustment
had to be repeated. The datum was sinking at a very high velocity of 1.85 mm/yr, which caused
unreasonably high uplifts in other datum BMs. After removing this BM from the datum list and
repeating the adjustment the solution changed markedly. The velocity of the tide gauge changed
in the opposite direction, from +0.15 to -0.30 mm/yr; the GPS BM velocity changed from +1.16
to +0.71 mm/yr. The final velocity of FSM3 was very high at -2.30 mm/yr.
In Fiji, the velocity of the fundamental BM, BM3243, was -0.45 mm/yr whereas the other
datum points, BM3244/5 had velocities of +0.20 and +0.25 mm/yr, respectively. This implies
that the fundamental BM is sinking at a considerably higher rate compared to the other points.
Similar case is encountered for BM26 in Cook Is. Both these marks are in coastal areas in
reclaimed land, which could explain their high velocities. However, their removal would result in
only two datum points, which is not acceptable, as results would be unreliable since it would be
difficult to detect relative movement in case one of the points becomes unstable. A preferred
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approach for the future would be to bring the initial epoch forward in order to use more of the
newer deep driven BMs as datum points.
The datum BMs in Kiribati, Manus Is (PNG), Nauru, Solomon Is, Tonga and Tuvalu
were relatively stable with the sum of their velocities less than 0.1 mm/yr. In Samoa, all datum
points had low relative velocities. However, BM201 and BM210, which are closer to the coast,
had slightly higher velocities at 0.4 mm/yr, compared to the inlands BMs, which had velocities
less than 0.2 mm/yr. The Vanuatu datum points VAN3 and VAN100 had velocities of -0.17 and
-0.18 mm/yr, whereas VAN101 had a velocity of +0.35 mm/yr. Even tough the nett velocity
amongst these three stations is zero; there was a considerable relative motion amongst them.
In the initial adjustment for Marshall Islands, MAR15 had a high vertical velocity at -
1.13 mm/yr compared to the lower velocity of -0.38 mm/yr for MAR3 and the other datum point.
This caused an unrealistically high velocity of -1.01 mm/yr of the tide gauge. Thus, MAR15 had
to be removed from the datum list and the initial epoch was brought forward to 2003. This
allowed the inclusion of BMs MAR51-52 to the datums list and the estimated velocity of the tide
gauge was reduced to almost zero. This shows that the tide gauge is relatively stable in relation
to the land mass.
Comparison with ITRF2008 Results
Table 5 shows discrepancies between the vertical velocity of the CGPS stations from the
levelling and the ITRF2008 solution, with an average RMS value of 2.4 mm/yr. The ITRF2008
is a globally consistent reference frame in an earth centred; earth fixed system, whereas the
levelling velocities from the proposed method are relative to a group of datum benchmark BMs
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in the local area. The high differences, particularly in Tonga and Vanuatu are due to
deformations in the local area, relative to the global reference frame. This could be due to
unmodelled earthquake effects as well as errors in levelling measurements However, a
meaningful comparison between the two datums is not viable since the velocities from the
proposed method are statically insignificant.
Examining the time series of the ITRF2008 residuals for each station revealed that there
were several gaps in the time series solutions for the CGPS stations. This may be due to delays in
providing the GPS data from the SPSLCMP network to the International GNSS Service (IGS)
analysis centres in time for processing. Annual and semi-annual seasonal signals were visible in
the time series, particularly in the height component, which is typical in GPS time series (Amiri-
Simkooei et al., 2007; Teferle et al., 2007; El-Mowafy, 2009). These are likely to be due to
residual ocean or atmospheric loading effects, which are not accurately accounted for in the
GNSS processing (Altamimi and Collilieux, 2009).
It is possible to apply the difference in the velocities between the levelling and ITRF2008
solutions as a correction for the local deformation with respect to the global frame. However, the
RMS of the transformed heights with respect to the constant velocity modelled heights is quite
high for some stations, as shown in Table 4. This shows that the motion of the GPS BM is non-
linear and possibly affected by geophysical effects, which cannot be measured by levelling since
the 1.5 year interval in-between surveys is too long compared to the frequency of geophysical
effects. Similar problems were encountered in Tervo et al. (2006). Therefore, it is highly
recommended to implement more continuous monitoring of the tide gauge stability. One
possibility is the dual-CGPS concept (Teferle et al., 2002), where a CGPS station is established
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at the tide gauge, while another station is located on stable rock within a few kilometres of the
tide gauge. By analysing the time series of the two co-located stations, spatial correlations can be
removed by differencing their positions to obtain a cleaner time series of vertical land motion.
This is especially required wherever the tide gauges are in a disturbed area, or if their area
experience frequent earthquakes and significant geophysical signals.
6. Conclusions
The vertical velocities of the tide gauges have been calculated successfully in a group of South
Pacific Countries with their respective uncertainties estimated from the repeated levelling and
EDM trigonometric height traversing. The approach was based on an inner constraint adjustment
that assumed constant velocities for modelling the vertical motion of the used BMs. Stability of
individual deep BMs was also confirmed. It was shown that except Solomon Is, none of the tide
gauges show significant motion relative to their CGPS BMs at the 95% confidence level.
However, the velocity for Solomon Is must be treated with caution due to the recent
establishment of the CGPS stations. Further analysis of levelling measurements from future
surveys may produce statistically significant motion of tide gauge BMs, by reducing the velocity
uncertainties.
The velocity of the tide gauge in Tonga was affected by a possible collusion of the tide
gauge with a ship whereas the Cook Is BMs were likely to be affected by errors in the 2002
survey. The effects of earthquakes and localised disturbances were removed in Vanuatu, Manus
Is (PNG) and Cook Is.
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In terms of how well the constant velocity model fits the observations at the tide gauges,
large deviations were found in Tonga and Cook Is due to local deformations and survey errors.
This model is not appropriate for tide gauges at Fiji, Marshall Is and Vanuatu, as there seems to
be some variability in their motion. As for the CGPS BMs, large deviations of few millimetres
were present in all cases. This is probably due to high frequency geophysical effects at the CGPS
BM which cannot be measured by the levelling method since they occur more frequently than
the 1.5 years between surveys.
Continuously measuring the tide gauge movements through implementing the dual-CGPS
concept is a promising approach for monitoring the tide gauge stability, especially where they
are disturbed by earthquakes and geophysical signals, e.g., at Vanuatu, Cook Islands. This will
allow the determination of the exact date of disturbances to the tide gauges, which can be applied
to the sea level data related to the tide gauge.
Acknowledgements
The second author publishes with the permission of the Chief Executive Officer, Geoscience
Australia (GA). The comments and suggestions by Dr John Dawson are most valued. This study
made use of levelling data collected collaboratively by staff of GA, National Tidal Facility,
Australia (NTF) and Secretariat of the Pacific Community (SOPAC) with funding from AusAID.
The authors thank the survey team including Steven Turner, Brian Ratcliff, Bob Twilley, Steve
Yates, Andrick Lal, Nick Brown and Guorong Hu.
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Appendix A
Table 6 gives Comparison of offsets between the CGPS BM and the tide gauge obtained by
direct measurements and from the inner constraint adjustment. The standard deviations () for
the measured offsets are based on first order levelling standards whereas for the adjusted offsets,
they are derived from the least-squares adjustment.
Table 6: Comparison of offsets between the CGPS BM and the tide gauge obtained by direct
measurements and from the inner constraint adjustment.
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Table 1: Installation dates for the tide gauge sensors and CGPS stations in the South Pacific, with
the distance between them along the levelling route.
Location Tide Gauge Sensor
installation CGPS station
installation Levelling
distance
between the tide
gauge and GPS
(km)
Cook Is Feb 1993 Sep 2001 1.94
Fiji Oct 1992 Nov 2001 1.92
Kiribati Dec 1992 Aug 2002 2.27
Manus Is (PNG) Sep 1994 May 2002 1.09
Marshall Is May 1993 May 2007 2.08
Nauru Jul 1993 July 2003 3.81
Pohnpei (FSM) Dec 2001 May 2003 3.47
Samoa Feb 1993 July 2001 5.04
Solomon Is Jul 1994 Jun 2008 1.31
Tonga Jan 1993 Feb 2002 1.17
Tuvalu Mar 1993 Dec 2001 3.47
Vanuatu Jan 1993 Sep 2002 3.43
Table 2: Details of the levelling surveys in each country. The epochs for which the tide gauges
were connected to the CGPS BMs are shown in bold font in the second column. The
fundamental BMs which were previously held fixed are shown in bold font in the last column.
Country Epochs of survey Datum points
Cook Is Feb 1993, Dec 1994, June 1996, June 1998,
Nov 1999, Jun 2001, Nov 2002, Aug 2004
(Comparison), Jan 2007, Jun 2008, Dec 2009
3 (BM26,
BM27, BM28)
Fiji Oct 1992, Aug 1994, Nov 1995, Jun 1997, Nov
1998, Dec 2000, Mar 2002, May 2003, May
2005 (Comparison), Feb 2007, Sep 2008, Feb
2010
3 (BM3243,
BM3244-5)
Kiribati Dec 1992, Mar 1994, Mar 1995, Sep 1996, Dec
1997, Jun 1999, Aug 2000, June 2002, May
2004, Mar 2006 (Comparison), Nov 2007,
3 (KIR1, KIR2-
3)
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Mar 2009, Sep 2010
Manus Is (PNG)
Aug 1994, Mar 1996, Sep 1997, Mar 1999, Nov
2000, May 2002, Sep 2003, Jan 2006
(Comparison), Aug 2007, Jun 2009, Dec 2010
2 (PNG1,
PNG3)
Marshall Is May 1993, Jun 1994, July 1995, Dec 1996, Aug
1998, Apr 2000, Sep 2001, Feb 2003, May
2006 (Comparison), Oct 2007, Apr 2009, Oct
2010
4 (MAR3,
MAR50-52)
Nauru Jul 1993, Mar 1994, Mar 1995, Sep 1996, Dec
1997, Jun 1999, Aug 2000, Jun 2002, Nov
2003, Oct 2005 (Comparison), Jun 2007, Feb
2009, Jul 2010
3 (NAU1,
NAU2,
NAU16)
Pohnpei (FSM) Dec 2001, Mar 2003, June 2006
(Comparison), Mar 2008, Aug 2009 5 (FSM1,
FSM2-5)
Samoa Oct 1993, Nov 1994, Jun 1996, Aug 1998, Nov
1999, Jun 2001, Dec 2002, Sep 2004, Oct 2006
(comparison), May 2008, May 2010
7 (BM201,
BM210,
BM212-5,
SAMOBM)
Solomon Is Aug 1994, Feb 1996, Aug 1997, Mar 1999,
Aug 2007, May 2009, Nov 2010 3 (FBM4,
FBM3, FBM1)
Tonga Jan 1993, Sep 1994, Nov 1995, Jun 1997, Nov
1998, May 2000, Feb 2002, Jun 2003, June
2005 (Comparison), Mar 2007, Oct 2008, Apr
2010
3 (TON1,
TON2-3)
Tuvalu Mar 1993, Jun 1994, Jun 1995, Dec 1996, Jul
1998, Mar 2000, Aug 2001, May 2003, Sep
2005 (Comparison), Mar 2007, Jan 2009,
Aug 2010
3 (BM22,
BM24-25)
Vanuatu Jan 1993, Jan 1994, Mar 1995, Feb 1997, Mar
1998, Aug 1999, Mar 2001, Sep 2002, May
2004, Sep 2006 (Comparison), Apr 2008, Sep
2009
3 (VAN3,
VAN100-101)
Table 3: Initial heights and vertical velocity estimates, with standard deviations, of fundamental
datum BMs, CGPS BMs and the tide gauges at the 12 locations in the Pacific Islands. The
statistical significance of the parameters is assessed at the 95% confidence level. Also given are
the RMS of residuals and degrees of freedom for the least squares adjustment.
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Country
Residual
RMS
(mm)/
Degrees
of
Freedom
BM H(t0)
(m)
H(t0)
(mm) Velocity
(mm/yr)
Velocity
(mm/yr) Description
BM27 4.7407 - 0.32 0.11 Datum BM
COO56 2.6876 2.47 Statistically
insignificant Tide gauge
Cook Is 0.83/
80
CGPS BM 3.2576 9.84 Statistically
insignificant
BM3243 3.1285 - -0.45 0.08 Datum BM
FIJ 13 4.4316 1.11 Statistically
insignificant Tide gauge
Fiji 0.95/
76
CGPS BM 31.3285
3.74 Statistically
insignificant
KIR1 3.5334 - Statistically
insignificant Datum BM
KIR13 4.6319 1.88 Statistically
insignificant Tide gauge
Kiribati 0.52/
81
CGPS BM 4.4127 2.07 Statistically
insignificant
PNG1 2.2988 - Statistically
insignificant Datum BM
PNG14 4.5799 0.46 Statistically
insignificant Tide gauge
Manus
Is
(PNG)
0.66/
56
CGPS BM 37.6890
1.82 Statistically
insignificant
MAR3 1.6083 - Statistically
insignificant Datum BM
MAR14 2.7920 3.15 Statistically
insignificant Tide gauge
Marshall
Is 1.33/
31
CGPS BM 3.1418 4.86 Statistically
insignificant
NAU1 7.2930 - Statistically
insignificant Datum BM
NAU15 6.0033 0.78 Statistically
insignificant Tide gauge
Nauru 0.48/
74
CGPS BM 5.2538 16.72 Statistically
insignificant
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FSM1 2.4382 - Statistically
insignificant Datum BM
FSM55 4.0330 0.64 Statistically
insignificant Tide gauge
Pohnpei
(FSM) 0.85/
31
CGPS BM 38.0036
2.96 Statistically
insignificant
BM201 1.3292 - -0.44 0.15 Datum BM
SAM17 4.1634 0.90 -0.72 0.30 Tide gauge
Samoa 0.43/
38 CGPS BM 38.1882
1.41 Statistically
insignificant Datum BM
FBM4 3.6197 - -0.07 0.03 Datum BM
SOL18 3.5756 0.55 -0.36 0.06 Tide gauge
Solomon
Is 0.73/
28 CGPS BM 54.3598
7.28 -3.48 0.49
TON1 1.1186 - Statistically
insignificant Datum BM
TON16 3.8944 4.24 Statistically
insignificant Tide gauge
Tonga 1.05
76
CGPS BM 1.9816 15.92 Statistically
insignificant
BM22 3.2254 - Statistically
insignificant Datum BM
TUV20 4.4608 0.96 Statistically
insignificant Tide gauge
Tuvalu 0.55/
69
CGPS BM 2.7421 6.70 Statistically
insignificant
VAN3 23.5463
- Statistically
insignificant Datum BM
VAN16 5.0104 3.09 Statistically
insignificant Tide gauge
Vanuatu 0.62/
33
CGPS BM 32.9070
3.42 Statistically
insignificant
Table 4: RMS of deviations of the transformed height from the heights obtained by the proposed
constant velocity method.
Country RMS (mm) of
transformed height –


0
H +H

at the tide gauge
RMS (mm) of
transformed height –


0
H +H

at the CGPS BMs
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Cook Islands 2.16 1.14
Fiji 1.09 1.06
Kiribati 0.72 0.64
Manus Is (PNG) 0.74 1.53
Marshall Is 1.23 0.40
Nauru 0.85 1.66
Pohnpei (FSM) 0.72 2.20
Samoa 0.40 1.31
Solomon Is 0.39 3.32
Tonga 3.09 0.38
Tuvalu 0.51 1.19
Vanuatu 1.41 0.93
Table 5: Velocity (mm/yr), with standard deviation of the tide gauges, relative to is associated
CGPS BM, from the proposed method. The ITRF2008 vertical velocity and standard deviation of
the CGPS station, in the last column, are from Altamimi et al. (2011).
Country Tide gauge
velocity
(mm/yr)
CGPS BM
velocity
(mm/yr)
Velocity of tide
gauge wrt CGPS
(mm/yr)
ITRF2008 velocity
of CGPS station
(mm/yr)
Cook Islands 0.06 0.24 0.09  0.77 -0.03  0.81 0.6  0.1
Fiji 0.14  0.13 0.19  0.28 -0.05  0.31 0.3  0.2
Kiribati 0.05  0.20 0.04  0.18 0.01  0.27 -0.4  0.1
Manus Is
(PNG) -0.08  0.06 -0.20  0.15 0.12  0.16 0.2  0.2
Marshall
Islands 0.02  0.75 0.01  0.51 0.01  0.91 N/A
Nauru 0.14  0.13 0.47  1.26 -0.33  1.26 -1.2  0.2
Pohnpei
(FSM) -0.30  0.19 0.71  0.60 -1.01  0.63 -0.8  0.2
Samoa -0.72  0.30 0.22  0.38 -0.94  0.49 0.1  0.2
Solomon Is -0.36  0.06 -3.48  0.49 3.12  0.49 N/A
Tonga -0.38  0.46 -0.01  1.21 -0.38  1.29 2.2  0.3
Tuvalu -0.11  0.11 -0.01  0.49 -0.10  0.50 0.1  0.2
Vanuatu -0.44  0.98 0.40  0.56 -0.84  1.13 -3.5  0.3
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Table 6: Comparison of offsets between the CGPS BM and the tide gauge obtained by direct
measurements and from the inner constraint adjustment.
Country/
RMS
(mm)
Epoch
(yr) Measured
Offset
and  (m)
Adjusted
Offset
and 
(m)
Country/
RMS
(mm)
Epoch
(yr) Measured
Offset
and  (m)
Adjusted
Offset
and 
(m)
2002.9 -0.5693 ±
0.0014 -0.5702
± 0.0101 Pohnpei
(FSM)/
1.9
2003.2 -33.9696
± 0.0019 -33.9719
± 0.0030
2004.6 -0.5692 ±
0.0014 -0.5703
± 0.0101 2006.4 -33.9770
± 0.0019 -33.9752
± 0.0030
2004.6 -0.5698 ±
0.0014 -0.5703
± 0.0101 2006.4 -33.9776
± 0.0019 -33.9752
± 0.0030
2007.0 -0.5729 ±
0.0014 -0.5704
± 0.0101 2008.2 -33.9755
± 0.0019 -33.9769
± 0.0030
2008.5 -0.5715 ±
0.0014 -0.5704
± 0.0101 2009.6 -33.9775
± 0.0019 -33.9784
± 0.0030
Cook Is /
1.3.
2009.9 -0.5702 ±
0.0014 -0.5705
± 0.0101 Samoa/
1.3 2003.0 -34.0235
± 0.0022 -34.0248
± 0.0017
Fiji/ 0.9 2002.2 -26.8989
± 0.0014 -26.8973
± 0.0039 2004.6 -34.0262
± 0.0022 -34.0264
± 0.0017
2003.4 -26.8970
± 0.0014 -26.8974
± 0.0039 2006.8 -34.0306
± 0.0022 -34.0284
± 0.0017
2005.4 -26.8979
± 0.0014 -26.8975
± 0.0039 2006.8 -34.0292
± 0.0022 -34.0284
± 0.0017
2005.4 -26.8984
± 0.0014 -26.8975
± 0.0039 2008.4 -34.0306
± 0.0022 -34.0298
± 0.0017
2007.1 -26.8972
± 0.0014 -26.8976
± 0.0039 2010.4 -34.0304
± 0.0022 -34.0317
± 0.0017
2008.7 -26.8983
± 0.0014 -26.8977
± 0.0039 Solomon
Is / 3.2 2007.7 -50.7391
± 0.0011 -50.7436
± 0.0073
2010.2 -26.8965
± 0.0014 -26.8977
± 0.0039 2009.4 -50.7415
± 0.0011 -50.7384
± 0.0073
Kiribati /
0.5 2002.4 0.2197 ±
0.0015 0.2193 ±
0.0028 2010.9 -50.7325
± 0.0011 -50.7336
± 0.0073
2004.4
0.2194 ±
0.2193 ±
Tonga /
2002.2
1.9070 ±
1.9094 ±
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0.0015 0.0028 2.9 0.0011 0.0165
2006.2 0.2189 ±
0.0015 0.2194 ±
0.0028 2003.4 1.9069 ±
0.0011 1.9089 ±
0.0165
2006.2 0.2202 ±
0.0015 0.2194 ±
0.0028 2005.5 1.9070 ±
0.0011 1.9081 ±
0.0165
2007.9 0.2189 ±
0.0015 0.2194 ±
0.0028 2005.5 1.9054 ±
0.0011 1.9081 ±
0.0165
2009.2 0.2195 ±
0.0015 0.2194 ±
0.0028 2007.2 1.9128 ±
0.0011 1.9075 ±
0.0165
2010.7 0.2188 ±
0.0015 0.2194 ±
0.0028 2008.8 1.9097 ±
0.0011 1.9069 ±
0.0165
Manus Is
(PNG)/
1.7
2002.4 -33.1068
± 0.0010 -33.1082
± 0.0019 2010.3 1.9080 ±
0.0011 1.9063 ±
0.0165
2003.7 -33.1102
± 0.0010 -33.1080
± 0.0019 Tuvalu/
1.2 2003.4 1.7179 ±
0.0019 1.7176 ±
0.0068
2006.0 -33.1072
± 0.0010 -33.1078
± 0.0019 2005.7 1.7168 ±
0.0019 1.7174 ±
0.0068
2006.0 -33.1098
± 0.0010 -33.1078
± 0.0019 2005.7 1.7160 ±
0.0019 1.7174 ±
0.0068
2007.7 -33.1092
± 0.0010 -33.1076
± 0.0019 2007.2 1.7190 ±
0.0019 1.7172 ±
0.0068
2009.4 -33.1067
± 0.0010 -33.1074
± 0.0019 2009.1 1.7170 ±
0.0019 1.7171 ±
0.0068
2010.9 -33.1050
± 0.0010 -33.1072
± 0.0019 2010.6 1.7150 ±
0.0019 1.7169 ±
0.0068
Marshall
Is/ 1.1 2007.75
-0.3481 ±
0.0014 -0.3498
± 0.0058 Vanuatu/
5.8 2002.7 -27.9001
± 0.0019 -27.9047
± 0.0046
2009.25
-0.3492 ±
0.0014 -0.3498
± 0.0058 2004.6 -27.8984
± 0.0019 -27.9063
± 0.0046
2010.81
-0.3494 ±
0.0014 -0.3498
± 0.0058 2006.7 -27.9047
± 0.0019 -27.9081
± 0.0046
Nauru /
1.7 2003.9 0.7476 ±
0.0020 0.7463 ±
0.0167
2006.7 -27.9050
± 0.0019 -27.9081
± 0.0046
2005.8 0.7457 ±
0.0020 0.7457 ±
0.0167 2008.3 -27.9016
± 0.0019 -27.9094
2007.5 0.7445 ±
0.0020 0.7451 ±
0.0167
2009.1 0.7469 ±
0.0020 0.7446 ±
0.0167
2010.5 0.7414 ±
0.0020 0.7441 ±
0.0167
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