A high-resolution gravimetric geoid model for Japan from EGM2008 and local gravity data

Odera, Patroba Achola; Kuroishi, Yuki

doi:10.5047/eps.2011.11.004

Cited by 17 publications

(17 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In both grids, the differences were very large, much greater than the decimeter. However, it is known that the sd of Stokes's Integral over Japanese lands is subdecimetric as measured by Kuroishi (2009) and Odera et al (2012). Thus, this large deviation is mainly due to the errors of discretization of input and propagation of input uncertainties in FDM, see Eq.…”

Section: Comparison Of Stokes's Integral With Fdm and Fdm2mentioning

confidence: 99%

“…The boundary values of T or N can be determined by: spirit levelling (HOFMANN-WELLENHOF et al, 2006;SANSO and SIDERIS, 2013), a global geopotential model (PAVLIS et al, 2012;PAIL et al, 2011PAIL et al, , 2010, satellite altimetry if the region is over the seas (HOFMANN-WELLENHOF et al, 2006;SANSO and SIDERIS, 2013) or the remove-compute-restore technique (HOFMANN-WELLENHOF et al, 2006;SANSO and SIDERIS, 2013;ODERA et al, 2012) which can be based on ellipsoidal corrections (MARTINEC and GRAFAREND, 1997;ARDESTANI and MARTINEC, 2003;HIPKIN, 2004;NAJAFI-ALAMDARI et al, 2006). This way, T is determined from the linear system derived from Eq.…”

Section: Numerical Solution Of the Dirichlet Problem By Fdm And Fdm2mentioning

confidence: 99%

“…Current high resolution geoid models do not consider these corrections and show decimeter big uncertainties, e.g. JGEOID2008 with 17cm for Japan (KUROISHI, 2009;ODERA et al, 2012) and USGG2009 with as much as 32.1cm for US (WANG et al, 2011). Users of geoid models require at least a decimeter quality as for oceanographers and geophysicists (KUROISHI, 2009) or a 1cm quality as for geodesists (SANSO and SIDERIS, 2013;TAPLEY et al, 2004) which is hardly attainable without methods of improved accuracy.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On accurate geoid modeling: derivation of dirichlet problems that govern geoidal undulations and geoid modeling by means of the finite difference method and a hybrid method

Rio

2014

Bol. Ciênc. Geod.

View full text Add to dashboard Cite

The geoid is the reference surface used to measure heights (orthometric). These are used to study any mass variability in the Earth system. As the Earth is represented by an oblate spheroid (Ellipsoid), the geoid is determined by geoidal undulations (N) which are the separation between these surfaces. N is determined from gravity data by Stokes's Integral. However, this approach takes a Spherical rather than an Ellipsoidal Earth. Here it is derived a Partial Differential Equation (PDE) that governs N over the Earth by means of a Dirichlet problem and show a method to solve it which precludes the need for a Spherical Earth. Moreover, Stokes's Integral solves a boundary value problem defined over the whole Earth. It was found that the Dirichlet problem derived here is defined only over the region where a geoid model is to be computed, which is advantageous for local geoid modeling. Moreover, the method eliminates several of the sources of uncertainty in Stokes's Integral. However, estimates indicate that the errors due to discretization are very large in this new method which calls for its modification. So, here it is also proposed an RESUMO O geóide é a superfície de referência utilizada para se medire altitudes (ortométrica). Estas são utilizadas para estudar qualquer variação de massa no sistema terrestre. Como a Terra é representada por um esferóide oblatado (elipsóide), o geóide é determinado por meio de ondulações geoidais (N) que são a separação entre essas superfícies. N é determinado a partir de dados gravitacionais pela integral de Stokes. Todavia, esta abordagem considera uma Terra esférica ao invés de elipsóidica. Neste artigo é deduzida uma equação diferencial parcial (sigla em inglês PDE) que governa N ao redor da Terra por vias de um Problema de Dirichlet. Também mostra-se aqui um método para resolver esta PDE que dispensa a necessidade de uma Terra esférica. Além do mais, a Integral de Stokes resolve um problema de valor de contorno definido por toda a Terra. Descobriu-se que o Problema de Dirichlet aqui proposto está definido apenas ao longo da região de cálculo o que é vantajoso para modelamento local do geóide. Além do mais, o método elimina diversas das fontes de incertezas presentes na Integral de Stokes. Todavia, estimativas indicam que o erro devido à discretização é muito grande neste novo método o que pede por modificações. Sendo assim, aqui também propõe-se uma combinação ótima de técnicas por meio de um método Híbrido. Mostra-se que que este método híbrido atenua as incertezas do método das Diferenças Finitas. Além do mais, uma rigorosa análise de erros indica que o método Híbrido aqui proposto pode bem desempenhar melhor do que a Integral de Stokes. Palavras-chave: Modelagem do Geóide; Problema de Dirichlet no Elipsóide; Método das Diferenças Finitas; Integral de Stokes.

show abstract

Section: Comparison Of Stokes's Integral With Fdm and Fdm2mentioning

confidence: 99%

Section: Numerical Solution Of the Dirichlet Problem By Fdm And Fdm2mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On accurate geoid modeling: derivation of dirichlet problems that govern geoidal undulations and geoid modeling by means of the finite difference method and a hybrid method

Rio

2014

Bol. Ciênc. Geod.

View full text Add to dashboard Cite

show abstract

“…This technique is referred to as offsets method in this study. A comparative study of the two techniques (LSC and Kriging) in interpolation of gravity anomalies can be found in Odera et al (2012). Amos and Featherstone (2009) used a similar model for unification of vertical datums based on a quasi-geoid model in New Zealand.…”

Section: Planar Fitting and Offsets Methodsmentioning

confidence: 99%

Recovery of orthometric heights from ellipsoidal heights using offsets method over Japan

Odera

2015

Earth Planet Sp

Self Cite

View full text Add to dashboard Cite

One of the most important applications of a geoid model is a recovery of orthometric heights from ellipsoidal heights (normally obtained from GNSS). The application of the geoid model for recovering orthometric heights from ellipsoidal heights is normally achieved by fitting the geoid model to a local vertical datum. The fitting procedure is usually accomplished by least squares collocation (LSC), using planar or spherical covariance functions. This procedure warps the gravimetric geoid model onto the local vertical datum, hence the local geoid model derived by this procedure, though convenient for local applications, it is not an equipotential surface. We propose offsets method for practical orthometric height recovery from a geoid model. The proposed procedure is more realistic because it does not constrain the local geoid to be coincident to the local vertical datum. We compare the performance of plannar fitting and offsets methods over Japan using a cross-validation procedure. Results show that offsets method performs better than the normally used planar fitting in the recovery of orthometric heights from ellipsoidal heights using a geoid model. The standard deviations of the differences between established and converted orthometric heights at randomly selected GPS/levelling test points over Japan are ±4 and ±3 cm for planar fitting and offsets methods, respectively. The offsets method is therefore more appropriate for converting ellipsoidal heights to orthometric heights than the planar fitting in the area of study.

show abstract

“…Data sets described in Odera et al (2012) have been used in this study. We give only a summary of the data sets here.…”

Section: Determination Of Rigorous Orthometric Heights Over Japanmentioning

confidence: 99%

Comparison of Helmert and rigorous orthometric heights over Japan

Odera

2015

Earth, Planets and Space

Self Cite

View full text Add to dashboard Cite

The local vertical datum in Japan is based on the Helmert's approximation of mean gravity along the plumbline. However, determination of a rigorous orthometric height requires that the integral-mean value of gravity along the plumbline between the geoid and the Earth surface has to be known precisely. An attempt has been made to obtain rigorous orthometric heights at 816 GPS/levelling points distributed over four main islands of Japan (Hokkaido, Honshu, Shikoku and Kyushu) by applying corrections to the Helmert orthometric heights. The corrections to Helmert orthometric heights are evaluated from the differences between the integral-mean gravity and the approximate mean gravity along the plumbline. The corrections to Helmert orthometric heights vary from −30.9 cm to 0.0 cm with a mean value of −0.4 cm and standard deviation of ±1.7 cm. An improved high-resolution gravimetric geoid model covering four main islands of Japan from our previous study is used to compare the consistency of the two height systems to a regionally defined gravimetric geoid model. The standard deviation of the differences between gravimetric and GPS/levelling geoid undulations is ±7.5 cm, when Helmert orthometric heights are used. The standard deviation of the differences between gravimetric and GPS/levelling geoid undulations reduces to ±7.3 cm, when rigorous orthometric heights are used. This indicates that rigorous orthometric heights are more consistent with the gravimetric geoid model than Helmert orthometric heights.

show abstract

A high-resolution gravimetric geoid model for Japan from EGM2008 and local gravity data

Cited by 17 publications

References 21 publications

On accurate geoid modeling: derivation of dirichlet problems that govern geoidal undulations and geoid modeling by means of the finite difference method and a hybrid method

On accurate geoid modeling: derivation of dirichlet problems that govern geoidal undulations and geoid modeling by means of the finite difference method and a hybrid method

Recovery of orthometric heights from ellipsoidal heights using offsets method over Japan

Comparison of Helmert and rigorous orthometric heights over Japan

Contact Info

Product

Resources

About