Impact of DHM resolution on gravity anomalies and geoid undulations: case study for Egypt

Figures & data

Figure 1. The utilised gravity data set’s distribution.

Figure 2. The fine 3^′′×3^′′digital terrain model EGH13S03, after (Abd-Elmotaal et al. 2013). Units in [m].

Figure 3. The conventional remove-restore method.

Figure 4. The window remove-restore technique.

Table 1. Standard deviations for the effect of T/I masses on gravity for different resolutions of DHMs. Unites in mgal.

Coarse DHM Fine DHM	${30}^{\prime \prime }$	$3^{\prime }$
$1^{\prime \prime }$	23.48	23.49
$3^{\prime \prime }$	23.49	23.50
$6^{\prime \prime }$	23.50	23.51
${15}^{\prime \prime }$	23.51	23.51

Table 2. Range for the effect of T/I masses on gravity for different resolutions of DHMs. Unites in mgal.

Coarse DHM Fine DHM	${30}^{\prime \prime }$*${30}^{\prime \prime }$	$3^{\prime }$* $3^{\prime }$
$1{ }^{\mathrm{\prime \prime }}\ast 1^{\prime \prime }$	385.39	385.10
$3^{\prime \prime }$*$3^{\prime \prime }$	385.40	385.11
$6{ }^{\mathrm{\prime \prime }}\ast 6^{\prime \prime }$	385.41	385.12
${15}^{\prime \prime }$*${15}^{\prime \prime }$	385.16	384.87

Table 3. CPU time elapsed for computing the effect of terrain of gravity for different resolutions of DHMs. Unites in minute.

Coarse DHM Fine DHM	${30}^{\prime \prime }$	$3^{\prime }$
$1^{\prime \prime }$	409	360
$3^{\prime \prime }$	80	71
$6^{\prime \prime }$	42	25
${15}^{\prime \prime }$	27	5

Figure 5. Difference in gravity anomalies between using fine DHM $1^{\prime \prime }$ x$1^{\prime \prime }$ and using fine DHM $3^{\prime \prime }$ x $3^{\prime \prime }$ with the same coarse DHM ${30}^{\prime \prime }$ x${30}^{\prime \prime }$ [units in mgal].

Table 4. The statistics of the difference in the indirect effect between using fine DHM $1^{\prime \prime }$ x $1^{\prime \prime }$ with coarse DHM ${30}^{\prime \prime }$ x ${30}^{\prime \prime }$ and using other fine DHM$\mathit{s}$ with different coarse DHM [units in cm].

	S01S30-S01M03	S01S30-S03S30	S01S30-S06S30	S01S30-S15S30	S01S30-S03M03	S01S30-S06M03	S01S30-S15M03
Min	−0.40	−0.10	−0.10	−0.10	−0.40	−0.40	−0.40
Max	1.50	0.10	0.10	0.10	1.50	1.50	1.40
Range	1.90	0.20	0.20	0.20	1.90	1.90	1.80
Mean	0.06	0.00	0.00	0.00	0.06	0.06	0.06
Std	0.13	0.01	0.02	0.03	0.13	0.13	0.13

Figure 6. Difference in the indirect effect between using fine DHM $1^{\prime \prime }$ x $1^{\prime \prime }$ and using fine DHM $3^{\prime \prime }$ x $3^{\prime \prime }$ with the same coarse DHM ${30}^{\prime \prime }$ x ${30}^{\prime \prime }$ [units in cm].

Figure 7. Difference in the indirect effect between using fine DHM $1^{\prime \prime }$ x $1{ }^{\mathrm{\prime \prime }}$ with coarse DHM ${30}^{\prime \prime }$ x ${30}^{\prime \prime }$ and using fine DHM ${15}^{\prime \prime }$ x ${15}^{\prime \prime }$ with coarse DHM $3^{\prime }$ x $3^{\prime }$ [units in cm].

Table 5. The statistics of the difference in the gravity contribution $\left(g_{\mathit{red}}\right)$ using fine DHM $1^{\prime \prime }$x $1^{\prime \prime }$ with coarse DHM ${30}^{\prime \prime }$ X ${30}^{\prime \prime }$ and using the same fine DHMs with different coarse DHMs [Units in cm].

	S01S30-S01M03	S01S30-S03S30	S01S30-S06S30	S01S30-S15S30	S01S30-S03M03	S01S30-S06M03	S01S30-S15M03
Min	−3.27	−6.36	−10.12	−15.62	−8.82	−12.66	−18.12
Max	2.45	−3.10	−4.57	−6.73	−0.95	−2.49	−4.78
Range	5.72	3.25	5.55	8.89	7.87	10.17	13.34
Mean	−1.60	−4.48	−6.74	−10.59	−6.06	−8.37	−12.18
Std	1.03	0.68	0.96	1.48	1.47	1.75	2.31

Figure 8. Difference in gravity contribution when using fine DHM $1^{\prime \prime }$ x $1^{\prime \prime }$ and using fine DHM $3^{\prime \prime }$ x $3^{\prime \prime }$ with the same coarse DHM ${30}^{\prime \prime }$ x ${30}^{\prime \prime }$ [units in cm].

Figure 9. Differences in gravity contribution on geoid undulation between using fine DHM $1^{\prime \prime }$ x $1{ }^{\mathrm{\prime \prime }}$with coarse DHM ${30}^{\prime \prime }$ x ${30}^{\prime \prime }$ and using fine DHM ${15}^{\prime \prime }$ x ${15}^{\prime \prime }$ with coarse DHM ${30}^{\prime \prime }$ x ${30}^{\prime \prime }$ [units in cm].

Figure 10. Histogram for the differences in gravity anomalies contribution on geoid undulation between using fine DHM $1^{\prime \prime }$ x$1{ }^{\mathrm{\prime \prime }}$ with coarse DHM ${30}^{\prime \prime }$x${30}^{\prime \prime }$ and using different fine DHM with the same coarse DHMs resolutions [units in cm].

Figure 11. Histogram for the differences in gravity contribution on geoid undulation between using fine DHM $1^{\prime \prime }$ x $1{ }^{\mathrm{\prime \prime }}$ with coarse DHM ${30}^{\prime \prime }$ x ${30}^{\prime \prime }$ and using different coarse DHMs resolutions with the same fine DHMs resolutions [units in cm].

Table 6. The statistics of the difference in the geoid undulation between using fine DHM $1^{\prime \prime }$ x $1^{\prime \prime }$ with coarse DHM ${30}^{\prime \prime }$ x ${30}^{\prime \prime }$ and using the same fine DHM$\mathit{s}$ with different coarse DHM units in [cm].

	S01S30-S01M03	S01S30-S03S30	S01S30-S06S30	S01S30-S15S30	S01S30-S03M03	S01S30-S06M03	S01S30-S15M03
Min	−3.37	−6.36	−10.12	−15.62	−8.87	−12.66	−18.12
Max	2.69	−3.10	−4.57	−6.72	−0.68	−2.22	−4.49
Range	6.06	3.25	5.55	8.89	8.19	10.42	13.63
Mean	−1.54	−4.48	−6.74	−10.60	−6.00	−8.31	−12.12
Std	1.04	0.68	0.96	1.48	1.49	1.77	2.32

Figure 12. Difference in geoid undulations between using fine DHM $1^{\prime \prime }$ x$1^{\prime \prime }$ and using fine DHM $3^{\prime \prime }$ x $3^{\prime \prime }$ with the same coarse DHM ${30}^{\prime \prime }$ x${30}^{\prime \prime }$ [units in cm].

Figure 13. Difference in geoid between using fine DHM $1^{\prime \prime }$ x $1^{\prime \prime }$ with coarse DHM ${30}^{\prime \prime }$ x ${30}^{\prime \prime }$ and using fine DHM ${15}^{\prime \prime }$ x ${15}^{\prime \prime }$ with coarse DHM ${30}^{\prime \prime }$ x ${30}^{\prime \prime }$ [Units in cm].

Figure 14. Histogram for the differences in total geoid undulation between using fine DHM $1^{\prime \prime }$ x $1{ }^{\mathrm{\prime \prime }}$with coarse DHM ${30}^{\prime \prime }$ x ${30}^{\prime \prime }$ and using different fine DHM with the same coarse DHMs resolutions [units in cm].

Figure 15. Histogram for the differences in total geoid undulation between using fine DHM $1^{\prime \prime }$ x $1{ }^{\mathrm{\prime \prime }}$ with coarse DHM ${30}^{\prime \prime }$ x ${30}^{\prime \prime }$ and using different coarse DHMs resolutions with the same fine DHMs resolutions [units in cm].

Table 7. Statistics of differences between the computed geoid for Egypt and the corresponding ones from (El-Ashquer et al. 2016) as well as the GPS/levelling data obtained from HARN.

	Statistical parameters
Statics	min	max	average	std
	m	m	m	m
Computed geoid	9.821	19.588	14.460	2.812
N from El-AShquer	9.856	19.613	14.469	2.795
N from HARN	9.779	19.330	14.458	2.743
N from HARN-N from Al-Ashquer	−0.409	0.309	−0.006	0.197
N from HARN-N from our geoid	−0.320	0.239	−0.006	0.176

Abd-Elmotaal HA, Abd-Elbaky M, Ashry M. 2013. 30 meters digital height model for Egypt. VIII Hotine-Marussi Symposium; [17–22 June 2013]; Rome, Italy.

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El-Ashquer M, Elsaka B, El-Fiky G. 2016. On the accuracy assessment of the latest releases of GOCE satellite-based geopotential models with EGM2008 andterrestrial GPS/levelling and gravity data over Egypt. Int J Geosciences. 7(11):1323–1344. doi: 10.4236/ijg.2016.711097.

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