Journal of Global Positioning Systems (2004)
Vol. 3, No. 1-2: 322-330
Mitigating Residual Tropospheric Delay to Improve User’s Network-
Based Positioning
Tajul A. Musa, Jinling Wang, Chris Rizos, Young-Jin Lee
School of Surveying and Spatial Information Systems, the University of New South Wales, NSW, Australia
e-mail: [e-mail]; Tel: [phone]; Fax: [phone]
Azhari Mohamed
Department of Survey and Mapping, Malaysia, Jalan Semarak, 50578 Kuala Lumpur, Malaysia
e-mail: [e-mail]; Tel: [phone]; Fax: [phone]
Received: 15 November 2004 / Accepted: 3 February 2005
Abstract. Existing apriori tropospheric models are not
sufficiently accurate to remove tropospheric delay from
GPS observations. Remaining effects of residual
tropospheric delay need to be estimated to ensure high
accuracy and reliability of GPS positioning. Other
researchers have shown that implementations of network-
based positioning techniques can adequately model the
residual tropospheric delay as well as ionospheric delay
and orbit biases. However, the effectiveness in removing
residual tropospheric delay is highly dependent on the
degree to which the wet component from the troposphere
can be estimated or mitigated, an effect which shows
strong variation with time and space. The aim of this
paper is to illustrate the performance of an existing
apriori tropospheric model and to discuss some issues
concerning the estimation of the (total) tropospheric delay
in the equatorial area. Finally, the network approach is
applied to mitigate the effect of residual tropospheric
delay. Some preliminary results from test experiments
using GPS network data from an equatorial region, a
location with the highest effect of tropospheric delay, are
presented.
Key words: Residual tropospheric delay, zenith path
delay, network-based GPS positioning
1 Introduction
The two propagation mediums which contribute to signal
delay of satellite observations are the ionosphere and the
neutral atmosphere. The ionosphere is a dispersive
medium for microwave, i.e the refractivity depends on
the frequency of the propagation signal. The ionosphere
delay can be determined and eliminated (at least to first
order) by making observations on both GPS frequencies.
Meanwhile the neutral atmosphere delay is mainly
attributed to the earth’s troposphere layer. The
troposphere consists of dry gases and water vapour, and
is a non-dispersive medium to radio frequency. Therefore
the delay effect cannot be estimated in the same way as
that of the ionosphere.
The neutral atmospheric delay can be estimated by
integrating the tropospheric refractivity along the GPS
signal path through the atmosphere. This is referred to as
the tropospheric path delay. It is possible to separate
tropospheric refractivity into a hydrostatic component (or
simply known as “dry”) and a wet component, where the
former is due to the dry atmosphere and the latter due to
the presence of water vapour in the atmosphere. The
(total) troposphere path delay needs to be mapped along a
path of arbitrary orientation, which can be represented as
the product of zenith delay and a specified mapping
function. The simplest mapping function is approximated
by cosec of the elevation angle. There is a difference in
mapping of wet and dry components, but they differ very
slightly and in practice usually they are lumped into a
single mapping function. The (total) Zenith Path Delay
(ZPD) can be written as:
)()( θθ mZmZZPDwetdry += (1)
where Zdry and Zwet are the zenith dry delay and zenith wet
delay respectively, m(θ) is the mapping function with θ as
the satellite elevation angle (for m(θ)≈cosec(θ)). There
are many troposphere models that have been developed,
e.g, Saastamoinen, Hopfield, Davis, Lanyi and Chao.
Most of these models effectively model the zenith dry

Tajul: Mitigating Residual Tropospheric Delay to Improve User’s Network-Based Positioning 323
delay, which contributes about 80%-90% of the total
delay (Hoffman-Wellenholf et al., 1994). However, all
the models have difficulty in modelling the wet delay due
to the high spatial and temporal variability of the water
vapour . As a result, a residual tropospheric delay remains
in the measurements after application of the model.
Over the past few years network-based GPS positioning
has been widely discussed in the literature (e.g.
Wanninger, 2002; Chen et al., 2000; Landau et al., 2002;
Rizos and Han, 2003). External information about the
GPS measurement biases provided by the network
technique has enabled the performance of conventional
single reference station, carrier phase-based techniques to
be extended over longer baselines. This is possible
because the network technique attempts to model
distance-dependent errors (i.e, atmospheric and orbit
effects) in the local network (Han, 1997; Chen, 2001).
First section on this paper discusses the performance of
two apriori tropospheric delay models. Secondly,
problems of residual tropospheric delay are discussed and
some issues concerning the estimation of the (total)
tropospheric delay are mentioned. A review of the GPS
network-based positioning approach is given in the third
section. Section four describes how the network approach
can be used in order to mitigate the residual tropospheric
delay.
2 Testing on apriori tropospheric delay modelling
To test the performance of the apriori tropospheric delay
model, tests were conducted using GPS datasets in a
near-equatorial region of the earth. The data was
collected by stations of the Malaysia Active GPS System
(MASS) (Figure 1). The GPS double-differenced (DD)
measurement model based on the ionosphere-free (IF)
carrier phase combination is used to eliminate the
ionospheric delay effect. The data processing
methodology resolves the “wide-lane ambiguity” first and
then fixes the “narrow-lane ambiguity” during subsequent
processing (Rothacher and Mervart, 1996; Sun et al.,
1999). Therefore for long baselines, the tropospheric
delay will dominate the DD IF residual errors, assuming
that other errors (geometric errors and multipath) are
minimised (for example by using the precise GPS orbit
data, multipath-free location and precise receiver
coordinates). GPS data of Day of Year (DoY) 29/03 for a
24 hours span was processed by the method described
above. A Satellite elevation cut-off angle of 15º was used
for the analyses. Station IPOH is excluded in the test due
to bad observations.
Fig. 1 Part of the MASS (Peninsular Malaysia)
Two apriori tropospheric delay models were chosen for
the test: the Saastamoinen model and the Modified
Hopfield model. Both models used values that are derived
from a standard atmosphere model. The test methodology
is as follows; Test 1: no apriori model is applied; Test 2:
applying only the dry model; and Test 3: applying both
the dry and wet troposphere models. Time series of the
above tests are shown in Figure 2, Figure 3(a) and 3(b),
and Figure 4(a) and 4(b) for a selected baseline KTPK-
ARAU. Table 1 and Table 2 give details of the results.
KTPK-ARA U (396km )
No Tropo Model
-2
-1
0
1
2
5266852668.2552668.5 52668.7552669
MJD
DD IF Residuals (m)
Fig. 2 Test 1 (no apriori troposphere model)
From Figure 2 and Table 1, the differential tropospheric
delay can be observed as being as large as 1.5m and a
RMS of up to 0.3m if no apriori troposphere model is
applied. Comparing Figure 1 to Figure 3 and Figures 4, it
is clear that both apriori models can mitigate the
tropospheric delay, as the maximum value decreases to
0.2m and the RMS of DD IF residuals is 0.05m. This is
also true for the other baselines in the tests. The test
statistic in Table 1 also shows that the error increases
with baseline length, which confirms that the residual
(DD) tropospheric delay can be categorised as a distance-
dependent error. Results in Table 2 show that a 73%-87%
improvement is achieved after applying the dry model.
Only a small improvement (1%-2%) is observed by

324 Journal of Global Positioning Systems
applying both the dry and wet models. In general, the DD
IF residuals after applying the apriori model are between
0.03m to 0.05m, mostly due to the wet component. There
is no significant difference in the test results between the
two apriori troposphere models.
KTPK-A RAU ( 396km)
Dry Model Only (Mod. Hopfield)
-0.4
-0.2
0
0.2
0.4
5266852668.25 52668.5 52668.7552669
MJD
DD IF Residuals (m)
KTPK-ARAU (39 6k m )
Dry Mode l Only (Saas tom oin en)
-0.4
-0.2
0
0.2
0.4
5266852668.25 52668.5 52668.7552669
MJD
DD IF Residuals (m)
Fig. 3 Test 3(a) left, dry Modified Hopfiled model and Test 3(b) right, dry Saastamoinen model
KTPK-ARAU (396k m)
Dr y & We t Mo d e l (Mo d. Hopf ield )
-0. 4
-0. 2
0
0. 2
0. 4
5266852668.25 52668.552668.7552669
MJD
DD IF Residuals (m)
KTPK-ARAU (396km)
Dry & Wet M odel ( Saas t omoinen)
-0.4
-0.2
0
0. 2
0. 4
5266852668.25 52668.552668.7552669
MJD
DD IF Residuals (m)
Fig. 4 Test 4(a) left, dry and wet Modified Hopfiled model. Test 4(b) right, dry and wet Saastamoinen model
Tab. 1 Statistic of Test 1, Test 2 and Test 3 of DD IF measurements.Station KTPK as reference and station height is 99m
Stn
KTPK
to:
Length
(km)
Stn
HEIGHT
(m)
DD IF
RMS
NO
MODEL
(m)
DD IF
RMS
DRY
SAAS
(m)
DD IF RMS
DRY M.
HOPFIELD
(m)
DD IF RMS
DRY&WET
SAAS
(m)
DD IF RMS
DRY&WET
M.HOPFILED
(m)
ARAU 396 82 0.310 0.054 0.053 0.049 0.048
GETI 341 100 0.373 0.057 0.056 0.049 0.048
USMP 288 80 0.267 0.048 0.048 0.045 0.044
KUAL 285 45 0.254 0.040 0.040 0.034 0.034
UTMJ 278 19 0.221 0.053 0.052 0.047 0.047
KUAN 196 74 0.127 0.027 0.027 0.025 0.025
SEGA 136 75 0.104 0.028 0.028 0.025 0.025
Tab. 2 Percentage improvement after applying dry model only and dry & wet model for DD IF measurements
Stn
KTPK to:
DRY
SAAS
(%)
DRY
M.HOPFILED
(%)
DRY&WET
SAAS
(%)
DRY&WET
M.HOPFIELD
(%)
ARAU 82.6 82.9 84.2 84.5
GETI 84.7 85.0 86.9 87.1
USMP 82.0 82.0 83.1 83.5
KUAL 84.3 84.3 86.6 86.6
UTMJ 76.0 76.5 78.7 78.7
KUAN 78.7 78.7 80.3 80.3
SEGA 73.1 73.1 76.0 76.0

Tajul: Mitigating Residual Tropospheric Delay to Improve User’s Network-Based Positioning 325
3 Issues on residuals tropospheric delay
At this stage, it is clear that the apriori troposphere model
cannot effectively handle the residual tropospheric delay.
High accuracy GPS positioning requires the residuals to be
reduced through appropriate modelling. The approach
usually is to introduce additional unknown parameters in the
least square estimation process, and to, for example, solve for
one scale factor for every station per session. The estimation
of the scale factor tends to average the residual tropospheric
delay, thus improving the results. However, the scale factor
is only a constant offset to the apriori model and does not
reflect the time varying nature of the atmosphere.
Alternatively, a time-varying polynomial scale factor can be
introduced to estimate several troposphere parameters per
session. Another viable approach is to use stochastic
estimation to model using a first-order Gauss-Markov or
random walk process (Dodson et al., 1996).
To this extent, it is convenient to discuss the residual
tropospheric delay in the context of the total ZPD. The
estimated troposphere parameter together with the apriori
model value and associated mapping function gives the GPS
derived (total) ZPD. Typically the process of GPS ZPD
estimation requires a large network of GPS reference stations
to achieve a stable value of absolute ZPD (discussion in next
section). A good example is the global network of the
International GPS Service (IGS) which already is in use,
publishing 2 hour absolute ZPD values. This IGS estimate
should be included in the processing of regional/local GPS
network data to benchmark the ZPD value derived from
regional/local solution.
3.1 Absolute vs relative tropospheric delay
Relative delay is more important than absolute delay for GPS
positioning. Beutler et al. (1988) gave a rule of thumb that
relative delay causes height errors which are amplified by the
factor of cosec(θmin) (2.9 for θmin =20°). Meanwhile an
absolute delay of 10cm will cause scale biases of 0.05ppm in
the estimated baseline lengths (Rothacher and Mervart,
1996). However, an accurate and absolute ZPD value is
crucial for GPS meteorology applications. Equation 1
indicates that one of the important factors in total ZPD
estimation is the satellite elevation angle. Duan et al. (1996)
have shown that for small sized GPS networks, the total ZPD
is sensitive to relative ZPD but not to absolute ZPD. This is
due to the small elevation angle difference observed between
two GPS receivers in the network. On the other hand, a large
network is needed to have large elevation angle variations in
order to get a better estimation of the absolute ZPD.
To analyse the relationship between absolute and relative
delay and the network size, a few regional IGS stations
around the local MASS network were used (Figure 5). IGS
station NTUS however is treated as a local station
because of the small distance to the MASS network
(KTPK-NTUS is only 297km). This will give an
advantage to the MASS network analysis in order to
benchmark the absolute ZPD value to the IGS
estimate.
Fig. 5 Regional GPS network
Two weeks data were selected for the test, DoY204-
210/03 (Jul23-Jul29 03), i.e. during a dry month, and
DoY323-329/09 (Nov19-Nov25 03), i.e. during a wet
month. For this analysis, the precise IGS orbits were
used; satellite elevation cut-off angle was set at 10°,
15° and 20°; a simple cosec mapping function was
used and the precise coordinates of all the reference
stations were supplied by the network operator.
Tropospheric parameters were estimated as piecewise
linear functions at two hour intervals for all the
stations, using the BERNESE software (Rothacher
and Mervart, 1996). Only results for the case of 15°
cut-off elevation angle for station NTUS is shown in
Figures 6 (a) & 6(b), 7(a) & 7(b) and 8(a) & 8(b), for
both weeks. Table 3 and Table 4 give the statistics of
all the test results for station NTUS.
Inspecting Figures 6(a) and 6(b) and Table 3, it can be
found that the absolute ZPD value (compared to the
IGS value) derived from the regional network is
accurate to about 3mm (in the dry season) and 5mm
(in the wet season), in terms of RMS values when
compared to the local network. Figures 7(a) and 7(b)
show the extracted values of absolute ZPD for both
networks. All tests (different 20°, 15°, 10° cut-off
elevation angles) show that the differences between
the regional and local absolute ZPD are within 1-3mm
(in the dry season) and 5-8mm (in the wet season).
The higher elevation angle observed from regional
network can provide a better estimation of absolute
ZPD. Both local and regional absolute ZPD estimates
differ by about 18mm-32mm in their RMS to the IGS
values, where the maximum difference occurs during
the wet season for the 10° cut-off elevation angle.

326 Journal of Global Positioning System
Total Zenith Path Delay (15deg elev)
Jul23- Jul 29 03
2.3
2.35
2.4
2.45
2.5
2.55
2.6
2.65
2.7
204 205206 207 208209 210
DoY 03
Total ZPD (m)
IGS
REGIONAL
LOCAL
MODEL
Total Zenith Path Delay (15deg elev)
Nov29-Nov25 03
2. 3
2. 35
2. 4
2. 45
2. 5
2. 55
2. 6
2. 65
2. 7
323324 325 326327328 329
DoY 03
Total ZPD (m)
IGS
REGIONAL
LOCAL
MODEL
Fig. 6 6(a) left, dry season and 6(b) right, wet season of total ZPD for station NTUS derived from different network size. IGS value is
obtained from combined ZPD solution published by IGS. Saastamoinen apriori model ZPD value is used (derived from standard atmosphere
value)
Absol ut e ZPD (15deg el ev)
Jul23-Jul29 03
-0.1
-0. 08
-0. 06
-0. 04
-0. 02
0
0. 02
0. 04
0. 06
0. 08
0.1
204 205 206207208 209 210
DoY 03
Absolute Diff (m)
Regional
Local
Absolute Z PD (15deg elev)
Nov29-Nov25 03
-0.1
-0. 08
-0. 06
-0. 04
-0. 02
0
0. 02
0. 04
0. 06
0. 08
0.1
323324 325 326 327328 329
DoY 03
Absolute Diff (m)
Region al
Local
Fig. 7 7(a) left, dry season and 7(b) right, wet season of absolute total ZPD difference for station NTUS to absolute IGS value using different network
size
Relati ve ZPD (15deg elev)
Jul23-Jul29 03
-0. 1
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
0.1
204 205 206 207 208 209 210
DoY 0 3
Relative Diff (m)
Regional
Local
Relat ive ZPD (15deg el ev)
Nov29-Nov25 03
-0.1
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
0.1
323 324325 326 327 328 329
DoY 03
Relative Diff (m )
Regional
Loc al
Fig. 8 8(a) left, dry season and 8(b) right, wet season of relative total ZPD difference for station NTUS. Station KTPK taken as reference
Tab. 3 Statistic of absolute ZPD difference (to value published by IGS) for station NTUS
Dry Season
(Jul23-Jul29 03)
Wet Season
(Nov19-Nov25 03)
Elevation Network Mean
(m)
Stdv
(m)
RMS
(m)
Mean
(m)
Stdv
(m)
RMS
(m)
REGIONAL 0.005 0.024 0.024 -0.013 0.020 0.023 20º
LOCAL -0.001 0.024 0.024 -0.016 0.023 0.028
REGIONAL 0.016 0.015 0.019 0.006 0.017 0.018 15º
LOCAL 0.011 0.016 0.022 0.001 0.023 0.023
REGIONAL 0.014 0.016 0.021 0.019 0.014 0.024 10º
LOCAL 0.017 0.015 0.022 0.027 0.017 0.032

Tajul: Mitigating Residual Tropospheric Delay to Improve User’s Network-Based Positioning 327
Tab. 4 Statistic of relative ZPD difference for station NTUS, KTPK as reference station
Dry Season
(Jul23-Jul29 03)
Wet Season
(Nov19-Nov25 03)
Elevation Network Mean
(m)
Stdv
(m)
RMS
(m)
Mean
(m)
Stdv
(m)
RMS
(m)
REGIONAL -0.004 0.041 0.041 -0.024 0.023 0.033 20º
LOCAL -0.006 0.041 0.041 -0.026 0.024 0.035
REGIONAL -0.009 0.032 0.033 -0.027 0.023 0.035 15º
LOCAL -0.010 0.032 0.033 -0.027 0.023 0.035
REGIONAL -0.007 0.028 0.029 -0.021 0.019 0.029 10º
LOCAL -0.007 0.027 0.028 -0.021 0.019 0.028
Comparing Figures 8(a) and 8(b), there is almost no
difference seen for the relative ZPD value estimation
between both networks (also true in the dry and wet
seasons). Further confirmation is found by inspecting
Table 4 for the rest of the tests. Results in Table 4 also
show that the RMS of the relative delay after applying the
apriori model is between 0.03m to 0.05m, which agrees
with the result in Table 1. Thus, the delay needs to be
estimated and removed from the measurements to ensure
high accuracy positioning, especially in the context of
ambiguity resolution.
4 Review of n et w or k-based positioning technique
Based on the Linear Combination Method (LCM) (Han
and Rizos, 1996), the single-differenced functional model
for the virtual measurements with n reference stations can
be written as:
]...[ ,11,11,
1
mnnmmu
n
i
ii −−
=
∆++∆−∆=∆
∑
φαφαφφα (2)
where
φ
is the carrier phase observation, α
i is the weight
for the i reference station determined to be inversely
proportional to the distance from i reference stations to
the user station u, m is the master reference station and ∆
is the single-differenced operator. The second term on the
right hand side of Equation (2) is the network correction
for the single-difference. 
The DD functional model for the virtual measurements
can be derived from Equation (3) as:
∑
+
∇∆+∇∆=++−∇∆
=
∇∆
−−
n
i
ii
mumumnnmmu NpVV
1
,,,11,11, ]...[
φα
ε
λααφ
(3)
where V is defined as the DD residual vectors from the
master station (m) to the other reference stations after the
ambiguities (N) have been resolved,
]...[ ,11,11 mnnm VV −−
+
+
α
α
is the DD network corrections
term, ∑
=
∇∆
n
i
ii
1
φα
ε
is the DD linear combination carrier phase
observation noise, λ is the wavelength of the carrier wave,
p is the satellite position vector minus the station position
vector, and
∇
∆
is the DD operator. The virtual
measurement ambiguity then should be fixed to its
integer value.
In general, the network processing can be summarised in
four major steps (Tajul et al., 2003):
⇒ Processing Master-Reference Stations – to get fixed
residuals of master station to other reference stations
after fixing the network ambiguities.
⇒ Calculation of Network Corrections – the network
corrections were calculated through Linear
Combination Method (LCM), i.e by applying linear
interpolation techniques to the fixed residual vectors.
⇒ Generating the so-called “Virtual Measurements” –
the network corrections were applied to master-user
measurements, epoch-by-epoch and satellite-by-
satellite basis to form a new set of measurement (the
“virtual measurements”).
⇒ Fixing the ambiguities – from master to user station
This processing can be implemented in either the post-
processing or real-time modes.
5 Network ap p ro ach t o mitigate residuals
tropospheric delay
One of the reasonable assumptions used in the network
technique described above is that the residual
tropospheric delay (i.e after applying the apriori model)
should be mitigated to some extent through the
application of the LCM (Han, 1997). To this point, it is
not clear how good the network technique will mitigate
the residual tropospheric error. The reason is because the

328 Journal of Global Positioning System
network corrections provided by the network are lumped
together with other distance-dependence errors, mostly
dominated by the ionosphere. The performance of the
network technique to account for the residual
tropospheric delay can be studied using the DD IF
measurements explained in section 2, to replace Equation
(3). This technique was successfully applied by Zhang
(1999) in his study using the NetAdjust method. The
purpose is to generate only residual tropospheric delay
corrections from the network stations, and it should be
applied to the user’s station in order to asses the
performance of this technique.
For this study part of the MASS network, stations
ARAU, KUAL, KUAN, KTPK, SEGA and NTUS (IGS
station), were selected (Figure 1). The reason for
selecting only these stations is to avoid the computational
burden in generating the network corrections, however
the design still gives good coverage over the study area.
For this selected network design there are five (n = 5)
reference stations - KTPK is selected as a master station
and SEGA as the user station because of it location inside
the network (KTPK-SEGA is 136km). All the
measurements are handled in post-processing (static)
mode, the precise IGS orbits are used and the satellite
elevation cut-off angle was set to 10°. The procedure
used for this network processing strategy was:
¾ Generate n-1 DD IF residual vectors from the
network measurements using the methodology
described in section 2.
¾ Calculate the residual tropospheric delay corrections
from the network based on the LCM.
¾ Apply the corrections to the DD IF measurements at
the user site.
-0.05
-0.04
-0.03
-0.02
-0.01
0
0.01
0.02
0.03
52847.000 52847.002 52847.004 52847.006 52847.007
MJD
DD IF Residuals
No_Corr
With_Corr
Fig. 10 DD IF residuals (m) of Satellite pair PRN26-05
-0.06
-0.05
-0.04
-0.03
-0.02
-0.01
0
0.01
0.02
0.03
0.04
52847.000 52847.00352847.005 52847.008
MJD
DD IF Residuals
No_Corr
With_Corr
Fig. 11 DD IF residuals (m) of Satellite pair PRN26-30
RMS VALUE (m)
No_Corr =0.017
With_corr=0.010
Improve:43%
RMS VALUE(m)
No_Corr = 0.020
With_corr=0.013
Improve: 35%

Tajul: Mitigating Residual Tropospheric Delay to Improve User’s Network-Based Positioning 329
KTPK-SEGA (1 3 6k m )
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
0.25
52847.00000 52847.05000 52847.1000052847.15000 52847.20000 52847.25000
MJD
DD IF Residuals (m )
No_corr
With_corr
Fig. 12 DD IF residual of all satellites pairs
Figure 10 and Figure 11 show the DD IF residuals and
statistics for two satellite pairs PRN26-05 and PRN26-30.
Figure 12 shows all combinations before and after
applying the correction. An improvement of about 33%-
43% in the RMS value is found for both pairs, 33% in the
case of all combinations after applying the corrections,
confirming the effectiveness of the network technique in
mitigating the residual tropospheric delay.
6 Concluding remarks
Results from this study using data from the MASS
network and the regional IGS stations show that:
Apriori tropospheric models effectively removed the dry
delay of the tropospheric delay by up to 73%-87%. Small
improvement (1%-2%) is achieved after applying the wet
model, indicating the difficulty in modelling the wet
component (mostly due to high variations of water
vapour in this region).
Accuracy of absolute ZPD value estimation (compared to
the IGS values) using the regional network is found to be
better than 3mm (dry season) and 8mm (wet season)
compared to local network estimation. Meanwhile,
almost no difference is found for the relative ZPD value
estimation for both networks.
Residual tropospheric delay can be mitigated in user’s
location using the network approach, where
improvements of up to 33% have been achieved.
Acknowledgements: We gratefully thank Department of
Survey and Mapping Malaysia (DSMM) for providing us
with the data used in this study.
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T, and Geiger A (1988): Atmospheric refraction and other
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With_corr=0.020
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