scholarly journals Quality Estimates in Geoid Computation by EGM08

2011 ◽  
Vol 1 (4) ◽  
pp. 361-366 ◽  
Author(s):  
L. Sjüberg
Keyword(s):  
Geoid Determination ◽  
Commission Error ◽  
Mean Square ◽  
Terrestrial Gravity ◽  
Topographic Bias ◽  
Gravitational Model ◽  
High Degree ◽  
Harmonic Representation ◽  
Mean Gravity ◽  
Geoid Computation

Quality Estimates in Geoid Computation by EGM08The high-degree Earth Gravitational Model EGM08 allows for geoid determination with a resolution of the order of 5'. Using this model for estimating the quasigeoid height, we estimate the global root mean square (rms) commission error to 5 and 11 cm, based on the assumptions that terrestrial gravity contributes to the model with an rms standard error of 5 mGal and correlation length 0:01° and 0:1°, respectively. The omission error is estimated to—0:7Δg [mm], where Δg is the regional mean gravity anomaly in units of mGal.In case of geoid determination by EGM08, the topographic bias must also be considered. This is because the Earth's gravitational potential, in contrast to its spherical harmonic representation by EGM08, is not a harmonic function at the geoid inside the topography. If a correction is applied for the bias, the main uncertainty that remains is that from the uncertainty in the topographic density, which will still contribute to the overall geoid error.

scholarly journals A Numerical Study of the Analytical Downward Continuation Error in Geoid Computation by EGM08

2011 ◽  
Vol 1 (1) ◽  
pp. 2-8 ◽  
Author(s):  
L. Sjöberg ◽  
M. Bagherbandi
Keyword(s):  
Numerical Study ◽  
Analytical Continuation ◽  
Downward Continuation ◽  
The Pacific ◽  
Topographic Bias ◽  
Significant Difference ◽  
Topographic Potential ◽  
Zero Degree ◽  
High Degree ◽  
Geoid Computation

A Numerical Study of the Analytical Downward Continuation Error in Geoid Computation by EGM08Today the geoid can be conveniently determined by a set of high-degree spherical harmonics, such as EGM08 with a resolution of about 5'. However, such a series will be biased when applied to the continental geoid inside the topographic masses. This error we call the analytical downward continuation (DWC) error, which is closely related with the so-called topographic potential bias. However, while the former error is the result of both analytical continuation of the potential inside the topographic masses and truncation of a series, the latter is only the effect of analytical continuation.This study compares the two errors for EGM08, complete to degree 2160. The result shows that the topographic bias ranges from 0 at sea level to 5.15 m in the Himalayas region, while the DWC error ranges from -0.08 m in the Pacific to 5.30 m in the Himalayas. The zero-degree effects of the two are the same (5.3 cm), while the rms of the first degree errors are both 0.3 cm. For higher degrees the power of the topographic bias is slightly larger than that for the DWC error, and the corresponding global rms values reaches 25.6 and 25.3 cm, respectively, at nmax=2160. The largest difference (20.5 cm) was found in the Himalayas. In most cases the DWC error agrees fairly well with the topographic bias, but there is a significant difference in high mountains. The global rms difference of the two errors clearly indicates that the two series diverge, a problem most likely related with the DWC error.

scholarly journals The topographic bias in Stokes’ formula vs. the error of analytical continuation by an Earth Gravitational Model - are they the same?

2015 ◽  
Vol 5 (1) ◽  
Author(s):  
L. E. Sjöberg
Keyword(s):  
Gravity Anomaly ◽  
Spherical Harmonics ◽  
Analytical Continuation ◽  
Geoid Determination ◽  
Disturbing Potential ◽  
Solid Spherical Harmonics ◽  
Topographic Bias ◽  
Gravitational Model ◽  
Stokes Formula ◽  
Original Formula

AbstractGeoid determination below the topographic surface in continental areas using analytical continuation of gravity anomaly and/or an external type of solid spherical harmonics determined by an Earth GravitationalModel (EGM) inevitably leads to a topographic bias, as the true disturbing potential at the geoid is not harmonic in contrast to its estimates. We show that this bias differs for the geoid heights represented by Stokes’ formula, an EGMand for the modified Stokes formula. The differences are due to the fact that the EGM suffers from truncation and divergence errors in addition to the topographic bias in Stokes’ original formula.

scholarly journals The Uganda Gravimetric Geoid Model 2014 Computed by The KTH Method

2015 ◽  
Vol 5 (1) ◽  
Author(s):  
L. E. Sjöberg ◽  
A. Gidudu ◽  
R. Ssengendo
Keyword(s):  
Gravity Field ◽  
Gravity Data ◽  
Geoid Determination ◽  
Geopotential Model ◽  
Gravimetric Geoid ◽  
Geoid Model ◽  
Satellite Mission ◽  
Terrestrial Gravity ◽  
Gravity Field Recovery ◽  
Goce Satellite

AbstractFor many developing countries such as Uganda, precise gravimetric geoid determination is hindered by the low quantity and quality of the terrestrial gravity data. With only one gravity data point per 65 km2, gravimetric geoid determination in Uganda appears an impossible task. However, recent advances in geoid modelling techniques coupled with the gravity-field anomalies from the Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) satellite mission have opened new avenues for geoid determination especially for areas with sparse terrestrial gravity. The present study therefore investigates the computation of a gravimetric geoid model overUganda (UGG2014) using the Least Squares Modification of Stokes formula with additive corrections. UGG2014 was derived from sparse terrestrial gravity data from the International Gravimetric Bureau, the 3 arc second SRTM ver4.1 Digital Elevation Model from CGIAR-CSI and the GOCE-only global geopotential model GO_CONS_GCF_2_TIM_R5. To compensate for the missing gravity data in the target area, we used the surface gravity anomalies extracted from the World Gravity Map 2012. Using 10 Global Navigation Satellite System (GNSS)/levelling data points distributed over Uganda, the RMS fit of the gravimetric geoid model before and after a 4-parameter fit is 11 cm and 7 cm respectively. These results show that UGG2014 agrees considerably better with GNSS/levelling than any other recent regional/ global gravimetric geoid model. The results also emphasize the significant contribution of the GOCE satellite mission to the gravity field recovery, especially for areas with very limited terrestrial gravity data.With an RMS of 7 cm, UGG2014 is a significant step forward in the modelling of a “1-cm geoid” over Uganda despite the poor quality and quantity of the terrestrial gravity data used for its computation.

scholarly journals Geoid determination with Hotine’s integral based on terrestrial gravity data in Semarang city

2019 ◽  
Vol 1127 ◽  
pp. 012047
Author(s):  
L. M. Sabri ◽  
Leni S. Heliani ◽  
T. A. Sunantyo ◽  
Nurrohmat Widjajanti
Keyword(s):  
Gravity Data ◽  
Geoid Determination ◽  
Terrestrial Gravity ◽  
Hotine’S Integral

scholarly journals The topographic bias in gravimetric geoid determination revisited

2019 ◽  
Vol 9 (1) ◽  
pp. 59-64
Author(s):  
Lars E. Sjöberg
Keyword(s):  
Density Distribution ◽  
Geoid Determination ◽  
The Other ◽  
Harmonic Potential ◽  
Gravimetric Geoid ◽  
Potential Bias ◽  
Computation Point ◽  
Density Distributions ◽  
Topographic Bias ◽  
Topographic Potential

Abstract The topographic potential bias at geoid level is the error of the analytically continued geopotential from or above the Earth’s surface to the geoid. We show that the topographic potential can be expressed as the sum of two Bouguer shell components, where the density distribution of one is spherical symmetric and the other is harmonic at any point along the normal to a sphere through the computation point. As a harmonic potential does not affect the bias, the resulting topographic bias is that of the first component, i.e. the spherical symmetric Bouguer shell. This implies that the so-called terrain potential is not likely to contribute significantly to the bias. We present three examples of the geoid bias for different topographic density distributions.

Classifying children with heavy prenatal alcohol exposure using measures of attention

2004 ◽  
Vol 10 (2) ◽  
pp. 271-277 ◽  
Author(s):  
KARA T. LEE ◽  
SARAH N. MATTSON ◽  
EDWARD P. RILEY
Keyword(s):  
Child Behavior Checklist ◽  
Prenatal Alcohol Exposure ◽  
Alcohol Exposure ◽  
Attention Problems ◽  
Commission Error ◽  
Final Model ◽  
Model Classification ◽  
Prenatal Alcohol ◽  
Freedom From Distractibility ◽  
High Degree

Deficits in attention are a hallmark of the effects of heavy prenatal alcohol exposure but although such deficits have been described in the literature, no attempt to use measures of attention to classify children with such exposure has been described. Thus, the current study attempted to classify children with heavy prenatal alcohol exposure (ALC) and non-exposed controls (CON), using four measures of attentional functioning: the Freedom from Distractibility index from the Wechsler Intelligence Scale for Children–Third Edition (WISC–III), the Attention Problems scale from the Child Behavior Checklist (CBCL), and omission and commission error scores from the Test of Variables of Attention (TOVA). Data from two groups of children were analyzed: children with heavy prenatal alcohol exposure and non-exposed controls. Children in the alcohol-exposed group included both children with or without fetal alcohol syndrome. Groups were matched on age, sex, ethnicity, and social class. Data were analyzed using backward logistic regression. The final model included the Freedom from Distractibility index from the WISC–III and the Attention Problems scale from the CBCL. The TOVA variables were not retained in the final model. Classification accuracy was 91.7% overall. Specifically, 93.3% of the alcohol-exposed children and 90% of the control children were accurately classified. These data indicate that children with heavy prenatal alcohol exposure can be distinguished from non-exposed controls with a high degree of accuracy using 2 commonly used measures of attention. (JINS, 2004, 10, 271–277.)

scholarly journals Evaluation of Stereo Images Matching

2021 ◽  
Vol 318 ◽  
pp. 04002
Author(s):  
Ali Hasan Hadi ◽  
Abbas Zedan Khalaf
Keyword(s):  
Image Matching ◽  
Stereo Image ◽  
Mean Square ◽  
Image Pair ◽  
Stereo Images ◽  
Minimum Value ◽  
Local Point ◽  
Feature Based ◽  
High Degree ◽  
Matching Techniques

Image matching and finding correspondence between a stereo image pair is an essential task in digital photogrammetry and computer vision. Stereo images represent the same scene from two different perspectives, and therefore they typically contain a high degree of redundancy. This paper includes an evaluation of implementing manual as well as auto-match between a pair of images that acquired with an overlapped area. Particular target points are selected to be matched manually (22 target points). Auto-matching, based on feature-based matching (FBM) method, has been applied to these target points by using BRISK, FAST, Harris, and MinEigen algorithms. Auto matching is conducted with two main phases: extraction (detection and description) and matching features. The matching techniques used by the prevalent algorithms depend on local point (corner) features. Also, the performance of the algorithms is assessed according to the results obtained from various criteria, such as the number of auto-matched points and the target points that auto-matched. This study aims to determine and evaluate the total root mean square error (RMSE) by comparing coordinates of manual matched target points with those obtained from auto-matching by each of the algorithms. According to the experimental results, the BRISK algorithm gives the higher number of auto-matched points, which equals 2942, while the Harris algorithm gives 378 points representing the lowest number of auto-matched points. All target points are auto-matched with BRISK and FAST algorithms, while 3 and 9 target points only auto-matched with Harris and MinEigen algorithms, respectively. Total RMSE in its minimum value is given by FAST and manual match in the first image, it is 0.002651206 mm, and Harris and manual match provide the minimum value of total RMSE in the second image is 0.002399477 mm.

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