A data-driven approach to local gravity field modelling using spherical radial basis functions

Klees, R.; Tenzer, Róbert; Prutkin, I.; Wittwer, T.

doi:10.1007/s00190-007-0196-3

Cited by 88 publications

(57 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The optimal bandwidth of the Poisson wavelets was estimated in an iterative least-squares approach using Generalized Cross Validation (Golub et al 1979). The approach is very similar to the one of Klees et al (2007a) with the only difference being that no local refinement needs to be applied. The latter is justified by the relatively homogeneous coverage of the target area with satellite data.…”

Section: Grace Gravity Modelsmentioning

confidence: 99%

“…Some analysis centres such as DEOS (e.g., Klees et al 2007a), the Institute of Theoretical Geodesy (ITG) at the University of Bonn (e.g., Eicker 2008), the Goddard Space Flight Center (GSFC) (e.g., Rowlands et al 2005;Luthcke et al 2006), and others, compute solutions for specific areas of interest using spherical radial basis functions (SRBFs) or single layer densities (mascons) as an alternative to the spherical harmonic representation of surface mass change. These so-called regional solutions use overflight data exclusively over the region of interest.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Comparison of Global and Regional GRACE Models for Land Hydrology

et al. 2008

Self Cite

View full text Add to dashboard Cite

When using GRACE as a tool for hydrology, many different gravity field model products are now available to the end user. The traditional spherical harmonics solutions produced from GRACE are typically obtained through an optimization of the gravity field data at the global scale, and are generated by a number of processing centers around the world. Alternatives to this global approach include so-called regional techniques, for which many variants exist, but whose common trait is that they only use the gravity data collected over the area of interest to generate the solution. To determine whether these regional solutions hold any advantage over the global techniques in terms of overall accuracy, a range of comparisons were made using some of the more widely used regional and global methods currently available. The regional techniques tested made use of either spherical radial basis functions or single layer densities (i.e., mascons), with the global solutions having been obtained from the various major processing centers. The solutions were evaluated using a range of computed statistics over a selection of major river basins, which were globally distributed and ranged in size from 1 to 6 million km 2 .For one of the basins tested, the Zambezi, additional validation tests were conducted through comparisons against a custom designed regional hydrology model of the region. We could not prove that current regional models perform better than global ones. Monthly mean water storage variations agree at the level of 0.02 m equivalent water height. The differences in terms of monthly mean water storage variations between regional and global solutions are comparable with the differences among only global or regional solutions. Typically they reach values of 0.02 m equivalent water heights, which seems to be the level of accuracy of current GRACE solutions for river basins above 1 million km 123Surv Geophys (2008) 29:335-359 DOI 10.1007 The amplitudes of the seasonal mass variations agree at the sub-centimetre level. Evident from all of the comparisons shown is the importance that the choice of regularization, or spatial filtering, can have on the solution quality. This was found to be true for global as well as regional techniques.

show abstract

Section: Grace Gravity Modelsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Comparison of Global and Regional GRACE Models for Land Hydrology

et al. 2008

Self Cite

View full text Add to dashboard Cite

show abstract

“…Examples include: the densification of gravity measurements using land surveys or airborne surveys in remote areas Page 3 of 41 A c c e p t e d M a n u s c r i p t 3 (Forsberg et al 2000;Kern et al 2003;Hwang et al 2007;Scheinert et. al 2007); the investment in dedicated satellite gravity missions CHAMP (Reigber et al 2002) and GRACE (Tapley et al 2005), and in global high-resolution DTMs (Digital Terrain Models) derived from the SRTM (Shuttle Radar Topography Mission) (Bamler 1999); and the development of new methods and techniques for geoid computation (Gitlein et al 2004;Schmidt and Kusche 2005;Serpas and Jekeli 2005;Sjöberg 2005; Klees et al 2007;Prutkin and Klees 2007).…”

Section: Introductionmentioning

confidence: 99%

Mapping the geoid for Iberia and the Macaronesian Islands using multi-sensor gravity data and the GRACE geopotential model

Catalão

Sevilla²

2009

Journal of Geodynamics

View full text Add to dashboard Cite

To cite this version:J. Catalão, M.J. Sevilla. Mapping the geoid for Iberia and the Macaronesian Islands using multisensor gravity data and the GRACE geopotential model. Journal of Geodynamics, Elsevier, 2009, 48 (1) This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Iberia, and the Macaronesian Islands using multi-sensor gravity data and a GRACE derived Earth geopotential model. A high resolution gravity model, determined using least squares optimal interpolation of marine, land, and satellite derived gravity anomalies, was used to resolve the medium and short wavelengths of the geoid. Long wavelengths of the geoid were provided by the GRACE derived Earth geopotential model. The topographic effects were computed in the spectral domain using a high resolution (100 m) digital terrain model derived from SRTM mission data and cartographic charts. The remove-restore technique was used to compute the geoid model on a 1.5 arc minute grid, and the residual geoid height was computed using spherical FFT and a modified Stokes' kernel. The effects of different Earth tide models on the geoid were computed and analyzed.Comparison over the sea with an oceanographic geoid determined from CLS01 MSSH and Rio05MDT yield a relative accuracy of 8 cm, with larger differences close to the shoreline. Over land, comparisons with 1646 GPS/levelling marks indicate an overall precision of 8-10 cm and relative vertical datum offsets of up to 2 m. This new geoid model represents a significant improvement over existing geoid models, with a homogeneous relative accuracy of 8-10 cm over both marine and land areas, and exposes the inaccuracies of local vertical datums as references for studies of vertical deformation.

show abstract

“…The mathematical foundation of RBFs, the special RBFs known as spherical wavelets, and their application in multiscale analysis are given by, for example, , Schmidt (2001), Jekeli (2005), or Schmidt et al (2007). In later years, we have observed an increased use of RBFs for regional gravity modeling (Roland 2005;Klees et al 2008;Eicker 2008;Tenzer and Klees 2008;Wittwer 2009;Bentel 2013;Naeimi 2013;Bentel et al 2013a, b;Eicker et al 2014;Pock et al 2012;Bucha et al 2015Bucha et al , 2016Naeimi et al 2015;Farahani et al 2016;Lieb et al 2016).…”

Section: Introductionmentioning

confidence: 99%

On the equivalence of spherical splines with least-squares collocation and Stokes’s formula for regional geoid computation

Ophaug

Gerlach

2017

J Geod

View full text Add to dashboard Cite

This work is an investigation of three methods for regional geoid computation: Stokes's formula, leastsquares collocation (LSC), and spherical radial base functions (RBFs) using the spline kernel (SK). It is a first attempt to compare the three methods theoretically and numerically in a unified framework. While Stokes integration and LSC may be regarded as classic methods for regional geoid computation, RBFs may still be regarded as a modern approach. All methods are theoretically equal when applied globally, and we therefore expect them to give comparable results in regional applications. However, it has been shown by de Min (Bull Géod 69:223-232, 1995. doi:10.1007/BF00806734) that the equivalence of Stokes's formula and LSC does not hold in regional applications without modifying the cross-covariance function. In order to make all methods comparable in regional applications, the corresponding modification has been introduced also in the SK. Ultimately, we present numerical examples comparing Stokes's formula, LSC, and SKs in a closed-loop environment using synthetic noise-free data, to verify their equivalence. All agree on the millimeter level.

show abstract

A data-driven approach to local gravity field modelling using spherical radial basis functions

Cited by 88 publications

References 28 publications

A Comparison of Global and Regional GRACE Models for Land Hydrology

A Comparison of Global and Regional GRACE Models for Land Hydrology

Mapping the geoid for Iberia and the Macaronesian Islands using multi-sensor gravity data and the GRACE geopotential model

On the equivalence of spherical splines with least-squares collocation and Stokes’s formula for regional geoid computation

Contact Info

Product

Resources

About