scholarly journals GOCE gradients in various reference frames and their accuracies

2003 ◽  
Vol 1 ◽  
pp. 33-38 ◽  
Author(s):  
J. Müller ◽  
M. Wermut
Keyword(s):  
Gravity Field ◽  
Ocean Circulation ◽  
Reference Frames ◽  
Terrestrial Reference Frame ◽  
Second Derivatives ◽  
Gravitational Gradients ◽  
The Matrix ◽  
Along Track ◽  
Derivatives Of

Abstract. The objective of GOCE (Gravity Field and Steady-State Ocean Circulation Explorer) is the determination of the Earth’s gravity field with high spatial resolution. The main science sensor (the gradiometer) measures differential accelerations, from which the gravitational gradients, i.e. the matrix of the second derivatives of the gravitational potential, are derived. Some of them (the diagonal components of the gravitational tensor) are observed with highest accuracy, 4 mE/√Hz in a frequency range from 5 mHz to 100 mHz, whereas the off-diagonals are obtained less accurately. The gradients will be observed in the instrument frame, which approximates the along-track oriented, local orbital frame. For the transformation of the gradients in other frames (e.g. in the strictly earth-pointing frame or a local geodetic frame), the transformation parameters (orientation angles) and all components of the gravity tensor have to be known with sufficient accuracy. We show how the elements of the gravitational tensor and their accuracies look like in the various frames as well as their spectral behaviour, if only the GOCE observations are used for the transformation. Only V'zz keeps approximately its original accuracy in all frames discussed, except in the earth-fixed frame ITRF (International Terrestrial Reference Frame). Therefore we recommend to analyse the gradients as ‘close’ as possible in the observation frame.Key words. Satellite gradiometry, GOCE mission, reference frames, transformation errors

scholarly journals Unification of European height system realizations

2012 ◽  
Vol 2 (4) ◽  
pp. 343-354 ◽  
Author(s):  
A. Rülke ◽  
G. Liebsch ◽  
M. Sacher ◽  
U. Schäfer ◽  
U. Schirmer ◽  
...  
Keyword(s):  
Gravity Field ◽  
Ocean Circulation ◽  
Reference Frames ◽  
Satellite Gravity ◽  
Global Gravity ◽  
Height System ◽  
Regional Gravity ◽  
Gravity Recovery ◽  
Satellite Gravity Missions

AbstractA suitable representation of the regional gravity field is used to estimate relative offsets between national height system realizations in Europe. The method used is based on a gravimetric approach and benefits from the significant improvements in the determination of the global gravity field by the recent satellite gravity missions the Gravity Recovery and Climate Experiment (GRACE) and the Gravity field and steady-state Ocean Circulation Explorerr (GOCE). The potential of these missions for the unification of height reference frames is analyzed in terms of accuracy and spatial resolution. The results of the gravimetric approach are compared to the independent results of the geodetic leveling approach. Advantages and drawbacks of both methods are discussed.

Estimation of gravitational curvature through a deterministic approach and spectral combination of space-borne second-order gravitational potential derivatives

2020 ◽  
Vol 224 (2) ◽  
pp. 825-842
Author(s):  
Mohsen Romeshkani ◽  
Mohammad A Sharifi ◽  
Dimitrios Tsoulis
Keyword(s):  
Gravity Field ◽  
Ocean Circulation ◽  
Gravitational Potential ◽  
Vertical Component ◽  
Second Order ◽  
Combination Method ◽  
Deterministic Approach ◽  
Third Order ◽  
Satellite Altitude

SUMMARY Second- and third-order gravitational potential derivatives can be employed for the determination of the medium- and high-frequency parts of the Earth's gravity field. Due to the Gravity field and steady-state Ocean Circulation Explorer mission, second-order derivatives (SOD) in particular, express currently observed functionals of high accuracy and global coverage. Third-order derivatives (TOD), or gravitational curvature data, provide significant gravity field information when applied regionally. The absence of directly observed TOD data underlines the importance of investigating the relationship between SOD and TOD. This paper discusses the combination of simulated SOD in order to obtain TOD at satellite altitude by applying the spectral combination method. For the determination of TOD integral equations are developed that utilize SOD data at satellite altitude, thus extending the well-known Meissl spectral scheme. The performance of the derived mathematical models is investigated numerically for the test area of Himalayas and the Tibet region. Two different TOD computational strategies are examined. First, we define a deterministic approach that recovers TOD data from noise-free simulated SOD data. Results show that retrieved TOD data at satellite level reach an agreement of the level of 1 × 10−17 m−1s−2 when compared with the true TOD data. Secondly, we propose a new mathematical model based on the spectral combination of integral relations and noisy SOD data with Gaussian noise for recovering TOD. Integral estimators of biased and unbiased types are examined in the cases of SOD data at satellite altitude. The used vertical SOD components show differences between the recovered and true vertical TOD components in the order of 1 × 10−17 m−1s−2 in magnitude, proving the vertical–vertical component of SOD as the best for validating purposes.

Fast determination of surface water mass changes using regional orthogonal functions

2020 ◽  
Author(s):  
Guillaume Ramillien ◽  
Lucia Seoane
Keyword(s):  
Surface Water ◽  
Water Mass ◽  
Mass Density ◽  
Extended Kalman Filtering ◽  
Orthogonal Functions ◽  
Continental Hydrology ◽  
The Matrix ◽  
Range Rate ◽  
Along Track

<p>Approaches based on Stokes coefficient filtering and « mass concentration » representations have been proposed for recovering changes of the surface water mass density from along-track accurate GRACE K-Band Range Rate (KBRR) measurements of geopotential change. The number of parameters, i.e. surface triangular tiles of water mass, to be determined remains large and the choice of the regularization strategy as the gravimetry inverse problem is non unique. In this study, we propose to use regional sets of orthogonal surface functions to image the structure of the surface water mass density variations. Since the number of coefficients of the development is largely smaller than the number of tiles, the computation of daily GRACE solutions for continental hydrology, e.g. obtained by Extended Kalman Filtering (EKF), is greatly fastened and eased by the matrix dimensions and conditioning. The proposed scheme of decomposition is applied to the African continent where it enables to very localized sources of (sub-)monthly water mass amplitudes.</p>

Determination of first and second derivatives of progress curves in the case of unknown experimental error

1990 ◽  
Vol 23 (5) ◽  
pp. 490-498 ◽  
Author(s):  
Rimantas Dagys ◽  
Saulius Tumas ◽  
Saulius Žvirblis ◽  
Algis Pauliukonis
Keyword(s):  
Experimental Error ◽  
Second Derivatives ◽  
Derivatives Of

scholarly journals Sensitivity of Goce Gradients on Greenland Mass Variation And Changes in Ice Topography

2014 ◽  
Vol 4 (1) ◽  
Author(s):  
M. Herceg ◽  
C. C. Tscherning ◽  
J. F. Levinsen
Keyword(s):  
Gravity Anomaly ◽  
Gravity Field ◽  
Ocean Circulation ◽  
Estimation Error ◽  
Least Squares Collocation ◽  
Grace Satellites ◽  
Residual Masses ◽  
Low Altitude ◽  
Gravity Signal

AbstractThe Gravity field and steady state Ocean Circulation Explorer (GOCE) maps variations in the gravity field by observing second order derivatives (gradients) of the Earth gravitational potential. Flying in the low altitude of 255 km and having a spatially dense data distribution of short wavelengths of the gravity field, GOCE may be used to enhance the time varying gravity signal coming fromthe GRACE satellites.The GOCE gradients may potentially be used for the determination of residual masses in local regions. This can be done using Least-Squares Collocation (LSC) or the Reduced Point Mass (RPM) method. In this study, different gravity field solutions are calculated by the use of RPM, LSC and GOCE gradients, respectively. Gravity field time series are created and presented for the six consecutive months of GOCE gradient observations, data being acquired between November 2009 and June 2010. Corresponding gravity anomaly results are used for the calculation of ice mass changes by the use of theRPMmethod. The results are then compared with the computed topographic effect of the ice by the use of a modified topographic correction and the Gravsoft TC program.The maximal gravity changes at the ground predicted from GOCE gradients are between 2 and 4 mGal for the period considered. The gravity anomaly estimation error arising from the GOCE gradient data using only T

scholarly journals The immobilization of enzymes on nylon structures and their use in automated analysis

1972 ◽  
Vol 129 (2) ◽  
pp. 255-262 ◽  
Author(s):  
D. J. Inman ◽  
W. E. Hornby
Keyword(s):  
Glucose Oxidase ◽  
Automated Analysis ◽  
Nylon Membrane ◽  
Nylon Tube ◽  
Immobilization Of Enzymes ◽  
The Matrix ◽  
Immobilized Glucose Oxidase ◽  
Derivatives Of ◽  
Automated Determination

1. Glucose oxidase (EC 1.1.3.4) and urease (EC 3.5.1.5) were covalently attached through glutaraldehyde to low-molecular-weight nylon powder. 2. Immobilized derivatives of glucose oxidase and urease were prepared by cross-linking the respective enzymes within the matrix of a nylon membrane. 3. An improved process is described for the immobilization of glucose oxidase and urease on the inside surface of partially hydrolysed nylon tube. 4. Automated analytical procedures are described for the determination of glucose with each of the three immobilized glucose oxidase derivatives and for the determination of urea with each of the three immobilized urease derivatives. 5. The efficiencies of the three immobilized enzyme structures as reagents for the automated determination of their substrates were compared.

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