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Investigation and comparison of RCR and LSMSA regional geoid modelling approaches

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In this study results will be presented on the numerical experiments and comparisons of two regional geoid modelling approaches: Remove-Compute-Restore (RCR) and Least Squares Modification of Stokes' Formula with Additive Corrections (LSMSA, also known as KTH). While RCR has been used for few decades, LSMSA approach has gained wide popularity in the last few years resulting in numerous national geoid solutions worldwide. Both approaches are having specific advantages and disadvantages as well as completely different computational strategies. The accuracy of solutions using both approaches shall be at the same level if identical data are used. However, several recent studies in different regions worldwide have shown LSMSA approach produced more optimal results than RCR approach. As it will be shown in this study, in the case of the Republic of Croatia, RCR approach produced slightly better solution compared to LSMSA approach. The analysis of results have led us to conclusion that geoid model accuracy is in large scope independent of the used approach and much more dependent on the selected parameters during modelling as well as on experience and expertise of the modeler. Finally, spatial distribution of differences and errors of computed models allowed us detection of problematic parts of the study area. Keywords: geoid, gravity, Remove-Compute-Restore (RCR), Least Squares Modification of Stokes’ Formula with Additive Corrections (LSMSA)
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10° 12 ° 14° 16° 18 ° 20° 22 °
40°
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48°
point gravity anomalies limits
gridded gravity anomalies limits
geoid model limits
-3° -1° 1° 3 ° 5° 7° 9°
42°
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point gravity anomalies limits
gridded gravity anomalies limits
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Ni=NiNi
g N
== +
egm2008
ITUGGC16
goconsgcf2timr5
goco05s
4.2
4.3
4.3
4.4
4.4
4.5
4.5
4.6
eigen6s4v2
ITUGGC16
goco05c
goco05s
GOSG01S
egm2008
ITSGGrace2014s
IfEGOCE05s
SGGUGM1
XGM2016
3.5
4.0
4.5
5.0
5.5
6.0
nmax= 200
nmax= 180
nmax= 150
NGNSS/lev .geoid n=
0 100 200 300 400 500 600 700 800
-10.0
0.0
10.0
20.0
30.0
40.0
eigen-6c4
egm2008
SGG-UGM1
XGM2016
NGNSS/lev .geoid n
0 0.5 1 1.5 2 2.5 3 3.5 4
-5.0
0.0
5.0
10.0
15.0
20.0
25.0
30.0
35.0
0 0.5 1 1.5 2 2.5 3 3.5 4
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40.0
50.0
60.0
nmax= 225
nmax= 650
nmax= 300
NGNSS/lev .geoid
0 2 4 6 8 10 12 14 16 18 20
2.0
2.5
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3.5
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NGNSS/lev .geoid
linear
nearest
natural
cubic
v4
3.5
3.5
3.6
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3.7
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3.8
3.9
linear
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natural
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3.6
3.6
3.6
3.6
3.6
NGNSS/lev .geoid
SRTM3
SRTM15
SRTM30
GTOPO30
ETOPO1
3.5
3.6
3.7
3.8
3.9
SRTM1
ASTER
AW3D30
SRTM15
ETOPO1
SRTM3
SRTM30
GTOPO30
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2.7
2.7
2.7
2.8
2.8
NGNSS/lev .geoid
BILINEAR
NEARESTNEIGHBOR
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BOX2X2
BOX9X9
3.5
3.5
3.6
3.6
3.7
3.7
3.8
3.8
BICUBIC
BILINEAR
NEAREST
BOX2X2
BOX9x9
3.7
3.8
3.8
3.9
NGNSS/lev .geoid
0 0.05 0.1 0.15 0.2
0.0
5.0
10.0
15.0
20.0
25.0
30.0
NGNSS/lev .geoid
0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
NGNSS/lev .geoid
n
ψ
C
std
... The expected accuracies from GOCE are of 1 mGal and 1-2 cm, respectively, for gravity anomalies and geoid, gravity field and the geoid, is computed from a pure satellite GGM (Omang & Forsberg, 2000). The accuracy of the achieved geoid depends on that of the used GGM and it is sensitive to d/o ranging from 150 and 250 (Varga, Grgic, Bjelotomić, & Bašić, 2018). The enhanced high-resolution combined GGMs by the residual terrain model (RTM) are also used for gravity database densification in areas with sparse data (Ulotu, 2009). ...
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