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The omission error modelling of global gravity field models using different digital terrain models

Martin Pitoňák1, Matej Varga2, Michal Šprlák1

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Gravity disturbances over test areas:

a) Czechia, b) Slovakia and c) southern

Colorado.

1NTIS – New Technologies for the Information Society, Faculty of Applied Sciences, University of West Bohemia, Pilsen, Czechia

2Institute of Geodesy and Photogrammetry, GSEG, ETH Zürich, Switzerland

The main goal of this contribution is to compare different approaches for modelling the omission error which could be one error source among many others in geoid determination. To do so we employ gravity disturbances over three test areas, namely, Czechia, Slovakia and southern Colorado. Firstly we subtract the high frequency part of gravitational field generated from the XGM2019e_2159 (Zingerle et al., 2019) model up to the degree 2160 terrestrial datasets. Then we will model the omitted signal in XGM2019e_2159 by (i) the topographic gravity field model dV_ELL_Earth_5480 (Rexer et al. 2017), (ii) the Earth’s short-scale gravity field models ERTM2160 (Hirt et al., 2014) and SRTM2gravity (Hirt et al., 2019) and by (iii) the forward modelling of residual topographic masses in spatial domain. Residual topographic masses were represented as differences between selected global (or near-global) digital elevation models such as AW3D30 (Tadano et al., 2014), ACE2 (Berry et al., 2010), MERIT DEM (Yamazaki et al., 2017), and SRTM 4.1 (Jarvis et al., 2008) and EARTH2014 (Hirt and Rexer 2015).

Results:

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�

b)

c)

 

XGM2019

dV_ELL_Earth_5480

AW3D30

ACE2

MERIT

SRTM4.1

ERTM2160

SRTM2gravity

CZECHIA

STD

11,152

8,102

9,568

9,718

9,741

9,642

7,287

7,282

MAX

50,773

52,409

47,210

47,169

47,045

47,277

51,868

52,203

MIN

-32,225

-33,327

-31,171

-31,514

-31,302

-31,371

-35,845

-36,247

MEAN

0,000

0,000

0,000

0,000

0,000

0,000

0,000

0,000

SLOVAKIA

STD

13,496

9,021

8,211

8,240

8,213

8,269

7,222

7,163

MAX

34,530

33,679

25,016

25,169

26,899

25,109

24,912

24,296

MIN

-46,546

-35,212

-32,283

-31,059

-30,783

-30,511

-39,004

-38,390

MEAN

0,000

0,000

0,000

0,000

0,000

0,000

0,000

0,000

COLORADO

STD

16,205

12,013

9,306

9,629

9,346

9,629

6,483

6,028

MAX

30,601

20,774

28,013

31,347

28,301

31,347

13,304

14,581

MIN

-52,763

-38,334

-20,787

-21,075

-20,982

-21,075

-17,702

-17,014

MEAN

0,000

0,000

0,000

0,000

0,000

0,000

0,000

0,000

RTM: r1=0.1° (polyhedron), r2=0.5° (prism), r3=1° (tesseroid), r4=5° (point-mass). In the fourth-zone we used ACE2 with spatial resolution of 9’’. We took advantage of TGF software (Yang et al., 2020).

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Conclusion:

  • the superior fit with respect to terrestrial data has been achieved from SRTM2gravity,
  • use of DEM with spatial resolution of 1’’ improved accuracy of omission error about 0.3 mGal in Colorado and 0.1 mGal in Czechia while there is no significant improvement in Slovakia,
  • the accuracy of omission error estimated from dV_ELL_Earth_5480 is questionable due to convergence of spherical harmonics below the Brillouin sphere.

a)

r = 6365478.5 m

r = 6366154 m

r = 6377176.353 m

Acknowledgment: This contribution was supported by project HR Award of University of West Bohemia and by the project No. 21-13713S of the Czech Science Foundation