scholarly journals Discrete Spherical Harmonic Transforms of Nearly Equidistributed Global Data

2011 ◽  
Vol 1 (3) ◽  
pp. 251-258 ◽  
Author(s):  
J. Blais
Keyword(s):  
Spherical Harmonic ◽  
Fourier Transforms ◽  
Simulated Data ◽  
Geopotential Model ◽  
Structural Constraints ◽  
Geopotential Models ◽  
Analysis And Synthesis ◽  
Comparative Results ◽  
Efficiency And Reliability ◽  
Global Data

Discrete Spherical Harmonic Transforms of Nearly Equidistributed Global DataDiscrete Spherical Harmonic Transforms (SHTs) are commonly defined for equiangular grids on the sphere. However, when global array data exhibit near equidistributed patterns rather than equiangular grids, discrete SHTs require appropriate adaptations for analysis and synthesis. Computational efficiency and reliability impose structural constraints on possible equidistribution characteristics of data patterns such as for instance with Chebychev quadratures and Fast Fourier Transforms (FFTs). Following some general introduction to discrete SHTs and equidistributions on the sphere, equitriangular (near equiareal) lattices based on the octahedron and the icosahedron are introduced for SHT analysis and synthesis. The developed formulations are described and implemented using simulated data and geopotential models such as the Earth Geopotential Model EGM 2008. Comparative results for analysis and synthesis at different levels of resolution show the potential of the spherical equitriangular approach for geodetic and other applications with nearly equidistributed global data.

scholarly journals Discrete Spherical Harmonic Transforms for Equiangular Grids of Spatial and Spectral Data

2011 ◽  
Vol 1 (1) ◽  
pp. 9-16 ◽  
Author(s):  
J. Blais
Keyword(s):  
Fourier Transform ◽  
Spectral Data ◽  
Spherical Harmonic ◽  
Fourier Transforms ◽  
Data Matrix ◽  
Geopotential Model ◽  
Double Precision ◽  
Analysis And Synthesis ◽  
Double Precision Arithmetic ◽  
Band Limited

Discrete Spherical Harmonic Transforms for Equiangular Grids of Spatial and Spectral DataSpherical Harmonic Transforms (SHTs) which are non-commutative Fourier transforms on the sphere are critical in global geopotential and related applications. Among the best known global strategies for discrete SHTs of band-limited spherical functions are Chebychev quadratures and least squares for equiangular grids. With proper numerical preconditioning, independent of latitude, reliable analysis and synthesis results for degrees and orders over 3800 in double precision arithmetic have been achieved and explicitly demonstrated using white noise simulations. The SHT synthesis and analysis can easily be modified for the ordinary Fourier transform of the data matrix and the mathematical situation is illustrated in a new functional diagram. Numerical analysis has shown very little differences in the numerical conditioning and computational efforts required when working with the two-dimensional (2D) Fourier transform of the data matrix. This can be interpreted as the spectral form of the discrete SHT which can be useful in multiresolution and other applications. Numerical results corresponding to the latest Earth Geopotential Model EGM 2008 of maximum degree and order 2190 are included with some discussion of the implications when working with such spectral sequences of fast decreasing magnitude.

scholarly journals Role of geo-potential models in gravity field determination

2009 ◽  
pp. 34-37
Author(s):  
Niraj Manandhar ◽  
Rene Forsberg
Keyword(s):  
Gravity Field ◽  
Geopotential Model ◽  
Potential Models ◽  
Geopotential Models ◽  
Gravity Field Determination ◽  
Major Emphasis

This paper sets out to describe the developments of geopotential models and its role in gravity field determination. The paper also focuses in different geopotential models those are available and in use from 1980 onwards till at present with major emphasis placed on WGS84 EGM96 geopotential model.

Streamlining Oceanic Biogeochemical Dataset Assembly in Support of Global Data Products

2020 ◽  
Author(s):  
Eugene Burger ◽  
Benjamin Pfeil ◽  
Kevin O'Brien ◽  
Linus Kamb ◽  
Steve Jones ◽  
...  
Keyword(s):  
Quality Control ◽  
Data Integration ◽  
Scientific Data ◽  
Climate Data ◽  
Science Data ◽  
Metadata Record ◽  
Data Products ◽  
Analysis And Synthesis ◽  
Data Integration System ◽  
Global Data

<p>Data assembly in support of global data products, such as GLODAP, and submission of data to national data centers to support long-term preservation, demands significant effort. This is in addition to the effort required to perform quality control on the data prior to submission. Delays in data assembly can negatively affect the timely production of scientific indicators that are dependent upon these datasets, including products such as GLODAP. What if data submission, metadata assembly and quality control can all be rolled into a single application? To support more streamlined data management processes in the NOAA Ocean Acidification Program (OAP) we are developing such an application.This application has the potential for application towards a broader community.</p><p>This application addresses the need that data contributing to analysis and synthesis products are high quality, well documented, and accessible from the applications scientists prefer to use. The Scientific Data Integration System (SDIS) application developed by the PMEL Science Data Integration Group, allows scientists to submit their data in a number of formats. Submitted data are checked for common errors. Metadata are extracted from the data that can then be complemented with a complete metadata record using the integrated metadata entry tool that collects rich metadata that meets the Carbon science community requirements. Still being developed, quality control for standard biogeochemical parameters will be integrated into the application. The quality control routines will be implemented in close collaboration with colleagues from the Bjerknes Climate Data Centre (BCDC) within the Bjerknes Centre for Climate Research (BCCR).  This presentation will highlight the capabilities that are now available as well as the implementation of the archive automation workflow, and it’s potential use in support of GLODAP data assembly efforts.</p>

Accuracy Assessment of Recent High-Degree Global Geopotential Models Using Geodetic Control Points and Terrestrial Gravity Data in Turkey

2021 ◽  
Author(s):  
Muhammed Raşit Çevikalp ◽  
Bihter Erol ◽  
Bilal Mutlu ◽  
Serdar Erol
Keyword(s):  
Gravity Data ◽  
Geopotential Model ◽  
Geoid Model ◽  
Terrestrial Gravity ◽  
Practical Applications ◽  
Geopotential Models ◽  
Vertical Datum ◽  
Height System ◽  
Orthometric Heights ◽  
Height System Unification

<p>The maintenance of leveling benchmark is both laborious and costly due to distortions caused by geodynamic activities and local deformations. It is necessary to realize geoid-based vertical datum, which also enables calculation from ellipsoidal heights obtained from GNSS to orthometric heights that have physical meaning. It can be considered as an important step for height system unification as it eliminates the problems stem from the conventional vertical datum. The ongoing height modernization efforts in Turkey focus to improve quality and coverage of the gravity data, eliminate errors in existing terrestrial gravity measurements in order to achieve a precise geoid model. Accuracy of the geopotential model is crucial while realizing a geoid model based vertical datum as well as unifying the regional height systems with the International Heights Reference System. In this point of view, we assessed the accuracies of recently released global geopotential models including XGM2019e_2159, GECO, EIGEN-6C4, EGM2008, SGG-UGM-1, EIGEN-6C3stat, and EIGEN-6C2 using high order GNSS/leveling control benchmarks and terrestrial gravity data in Turkey. The reason for choosing these models in the validations is their relatively higher spatial resolutions and improved accuracies compared to other GGMs in published validation results with globally distributed terrestrial data. The GNSS/leveling data used in validations include high accuracy GNSS coordinates in ITRF datum with co-located Helmert orthometric heights in regional vertical datum. 100 benchmarks are homogeneously distributed in the country with the benchmarks along the coastlines. In addition, the terrestrial gravity anomalies with 5 arc-minute resolution were also used in the tests. In order to have comparable results, residual terrain effect has been restored to the GGM derived parameters. Numerical tests revealed significant differences in accuracies of the tested GGMs. The most accurate GGM has the comparable performance with official regional geoid model solutions in Turkey. The drawn results in the study were interpreted and discussed from practical applications and height system unification points in conclusion.</p>

Transforms of Deterministic Continuous-Time Signals

2021 ◽  
pp. 599-673
Author(s):  
Stevan Berber
Keyword(s):  
Spectral Density ◽  
Continuous Time ◽  
Communication Systems ◽  
Fourier Transforms ◽  
Linear Time ◽  
Linear Time Invariant ◽  
Energy Spectral Density ◽  
Time Signals ◽  
Analysis And Synthesis ◽  
The Fourier Transform

Chapter 12 presents a detailed analysis of continuous-time signals and systems in the frequency domain, including the theory of Fourier series and Fourier transforms, and key examples relevant for the analysis and synthesis of signals processed in the digital transceiver blocks of a communication system. The amplitude, magnitude, phase, and power spectra are defined and calculated for typical signals. In particular, the Fourier transform of periodic signals is presented, due to its importance in communication systems theory and practice. Using a unique notation that distinguishes energy and power signals, the correlation, power, and energy spectral density functions are inter-related by proving the Wiener–Khintchine theorem. A comprehensive analysis of a linear-time-invariant system, using the concepts of impulse response, system correlation function, and power spectral density, both for power signals and energy signals, is presented. In addition, Parseval’s theorem and the Rayleigh theorem are proven.

scholarly journals Accuracy assessment of GOCE-based geopotential models and their use for modelling the gravimetric quasigeoid - A case study for Poland

2014 ◽  
Vol 63 (1) ◽  
pp. 3-24 ◽  
Author(s):  
Walyeldeen Godah ◽  
Malgorzata Szelachowska ◽  
Jan Krynski
Keyword(s):  
Gravity Field ◽  
Ocean Circulation ◽  
Accuracy Assessment ◽  
Gravity Anomalies ◽  
Geopotential Model ◽  
Satellite Gravity ◽  
Earth Gravity ◽  
Geopotential Models ◽  
Gravimetric Quasigeoid ◽  
Gravity Signal

Abstract The GOCE (Gravity Field and Steady-State Ocean Circulation Explorer) has significantly upgraded the knowledge on the Earth gravity field. In this contribution the accuracy of height anomalies determined from Global Geopotential Models (GGMs) based on approximately 27 months GOCE satellite gravity gradiometry (SGG) data have been assessed over Poland using three sets of precise GNSS/levelling data. The fits of height anomalies obtained from 4th release GOCE-based GGMs to GNSS/levelling data were discussed and compared with the respective ones of 3rd release GOCE-based GGMs and the EGM08. Furthermore, two highly accurate gravimetric quasigeoid models were developed over the area of Poland using high resolution Faye gravity anomalies. In the first, the GOCE-based GGM was used as a reference geopotential model, and in the second - the EGM08. They were evaluated with GNSS/levelling data and their accuracy performance was assessed. The use of GOCE-based GGMs for recovering the long-wavelength gravity signal in gravimetric quasigeoid modelling was discussed.

scholarly journals Ultra-high degree spherical harmonic analysis and synthesis using extended-range arithmetic

2007 ◽  
Vol 82 (4-5) ◽  
pp. 223-229 ◽  
Author(s):  
Tobias Wittwer ◽  
Roland Klees ◽  
Kurt Seitz ◽  
Bernhard Heck
Keyword(s):  
Harmonic Analysis ◽  
Spherical Harmonic ◽  
Spherical Harmonic Analysis ◽  
Extended Range ◽  
Analysis And Synthesis ◽  
High Degree

The digital zenith camera as an additional technique for quasi-geoid model determination of Latvia

2020 ◽  
Author(s):  
Katerina Morozova ◽  
Gunars Silabriedis ◽  
Ansis Zarins ◽  
Janis Balodis ◽  
Reiner Jaeger
Keyword(s):  
Geological Structure ◽  
Geopotential Model ◽  
Parametric Modelling ◽  
Vertical Deflection ◽  
Geoid Model ◽  
Star Catalog ◽  
Geopotential Models ◽  
Model Determination ◽  
The University

<p>The digital zenith camera VESTA (VErtical by STArs) was designed by the Institute of Geodesy and Geoinformatics (GGI) of the University of Latvia and completed in 2016. By 2020 more than 400 terrestrial vertical deflection measurements were observed in the territory of Latvia. These observations were post-processed by the GGI developed software and the accuracy was evaluated at 0.1 arc seconds. In 2019 two new cameras have been developed, which will be used in future projects, e.g., in determination of properties of local geological structure or Earth crust movement monitoring. Measurement control software corrections and complements, data processing improvements and automation and transition to GAIA data release 2 star catalog were done. The accuracy of the measurements of improved camera was evaluated at 0.05 arc seconds.</p><p>Terrestrial vertical deflection observations were compared with global geopotential models, e.g. GGM+ and EGM2008. The results show a better correspondence with GGM+ model by evaluating the standard deviation: 0.314 and 0.307 arc seconds for ξ and η components respectively in comparison to 0.346 and 0.358 arc seconds for ξ and η components for EGM2008 model. The comparisons of average and minimum/maximum differences are introduced in this study for better evaluation of the results. Moreover, vertical deflections have been used as additional terrestrial data in DFHRS (Digital Finite-element Height Reference Surface) software v. 4.3 in combination with GNSS/levelling data (B, L, hH) and global geopotential model EGM2008 for gravity field and quasi-geoid improvement (www.dfhbf.de). This approach is based on parametric modelling and computation of height reference surfaces (HRS) from geometric and physical observation components in a hybrid adjustment approach. The results of the computed quasi-geoid models using different types of data are introduced in this research, representing several solutions, as well as these solutions are compared with the national quasi-geoid model LV’14.</p>

Combining GGM and RTM to model the gravity gradient tensor

2020 ◽  
Author(s):  
Jinzhao Liu
Keyword(s):  
Spherical Harmonic ◽  
Shuttle Radar Topography Mission ◽  
Gravity Gradient ◽  
Geopotential Model ◽  
Gradient Tensor ◽  
Gravity Gradient Tensor ◽  
Terrain Model ◽  
Truncation Errors ◽  
Elevation Model ◽  
High Degree

<p>In this paper, by combining the Global Geopotential Model (GGM, specifically, EGM2008 is used) and the Residual Terrain Model (RTM) data, we have modeled the Gravity Gradient Tensor (GGT) in eastern Tian shan mountains areas, China. The RTM data are obtained from the Shuttle Radar Topography Mission (SRTM) elevation model and the DTM2006.0 high degree spherical harmonic reference surface. The integration of RTM data reduces the truncation errors (or called omission errors) due to the finite expansion terms of the spherical harmonic coefficients of the GGM, and compensates for the high frequency information and spatial resolution of the GGT within the study area.</p>

Assessment of the GOCE-Based Global Gravity Models in Canada

GEOMATICA ◽  
2012 ◽  
Vol 66 (2) ◽  
pp. 125-140 ◽  
Author(s):  
E. Sinem Ince ◽  
Michael G. Sideris ◽  
Jianliang Huang ◽  
Marc Véronneau
Keyword(s):  
Great Lakes ◽  
Rocky Mountains ◽  
Spherical Harmonic ◽  
Gravity Models ◽  
Geopotential Model ◽  
Third Generation ◽  
Combined Models ◽  
Gps Leveling ◽  
Global Gravity Models ◽  
Geoid Undulations

The aim of this study is to test the first, second and third generation GOCE geoid solutions, obtained from the first 2, 8 and 18-month observations, respectively. These solutions are assessed over Canada and for two sub-regions (the Great Lakes and Rocky Mountains). The Canadian GPS/leveling-derived geoid heights are used as independent control values in the assessment of the GOCE geoid models. The study is conducted in two steps. First, the geoid models are computed from satellite-only models and truncated to different spherical harmonic degrees. These models are compared with the GPS/leveling geoid heights which are reduced to the same spectral band as the satellite models by EGM2008 predicted frequency components higher than the truncation degrees. The results suggest that the GOCE models show a full power of signal up to about spherical harmonic degree 180. Moreover, the second and third generation GOCE models (with the exception of the direct approach models) provide better agreement with the GPS/leveling-derived geoid undulations than the first generation models due to the longer observation period. The second step involves the combination of the two third generation GOCE models with terrestrial data. These models are tested against to the GPS/leveling-derived geoid undulations in full spectrum. EGM2008 global geopotential model and Canadian gravimetric geoid model CGG2005 are also included in the comparisons to measure improvement provided by the GOCE models. The GOCE-combined models yielded GPS/leveling results that are comparable with those obtained from EGM2008 and CGG2005 models. The best comparative results with the combined models give standard deviations of 4.8 cm, 6.0 cm and 12.2 cm for the Great Lakes, Rocky Mountains and Canada, respectively. These results indicate that the third generation GOCE models conform to the Canadian terrestrial gravity data from degrees 90 to 180. The new generation models show evident improvement over the first and second generation models.

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