Validation of calibrated GOCE gravity gradients GRD_SPW_2 by least-squares spectral weighting   

2021 ◽  
Author(s):  
Martin Pitoňák ◽  
Michal Šprlák ◽  
Vegard Ophaug ◽  
Ove Omang ◽  
Pavel Novák
Keyword(s):  
Least Squares ◽  
Ocean Circulation ◽  
Directional Derivatives ◽  
Gravity Gradients ◽  
Terrain Model ◽  
Satellite Altitude ◽  
Gravitational Gradients ◽  
Gravity Disturbances ◽  
Spectral Weighting ◽  
Level 2

<p>The Gravity field and steady-state Ocean Circulation Explorer (GOCE) was the first mission which carried a novel instrument, gradiometer, which allowed to measure the second-order directional derivatives of the gravitational potential or gravitational gradients with uniform quality and a near-global coverage. More than three years of the outstanding measurements resulted in two levels of data products (Level 1b and Level 2), six releases of global gravitational models (GGMs), and several grids of gravitational gradients (see, e.g., ESA-funded GOCE+ GeoExplore project or Space-wise GOCE products). The grids of gravitational gradients represent a step between gravitational gradients measured directly along the GOCE orbit and data directly from GGMs. One could use grids of gravitational gradients for geodetic as well as for geophysical applications. In this contribution, we are going to validate the official Level 2 product GRD_SPW_2 by terrestrial gravity disturbances and GNSS/levelling over two test areas located in Europe, namely in Norway and former Czechoslovakia (now Czechia and Slovakia). GRD_SPW_2 product contains all six gravity gradients at satellite altitude from the space-wise approach computed only from GOCE data for the available time span (r-2, r-4, and r-5) and provided on a 0.2 degree grid. A mathematical model based on a least-squares spectral weighting will be developed and the corresponding spectral weights will be presented for the validation of gravitational gradients grids. This model allows us to continue downward gravitational gradients grids to an irregular topographic surface (not to a mean sphere) and transform them into gravity disturbances and/or geoidal heights in one step. Before we compared results obtained by spectral downward continuation, we had to remove the high-frequency part of the gravitational signal from terrestrial data because in gravitational gradients measured at GOCE satellite altitude is attenuated. To do so we employ EGM2008 up to d/o 2160 and the residual terrain model correction (RTC) has been a) interpolated from ERTM2160 gravity model, b) synthesised from dV_ELL_Earth2014_5480_plusGRS80, c) calculated from a residual topographic model by forward modelling in the space domain.  </p>

scholarly journals An evaluation of recent GOCE geopotential models in Brazil

2012 ◽  
Vol 2 (2) ◽  
pp. 144-155 ◽  
Author(s):  
G. Guimarães ◽  
A. Matos ◽  
D. Blitzkow
Keyword(s):  
Steady State ◽  
Ocean Circulation ◽  
Gravity Data ◽  
The Other ◽  
Entire Area ◽  
Terrestrial Gravity ◽  
Terrain Model ◽  
Geopotential Models ◽  
Gravity Disturbances ◽  
Rms Errors

An evaluation of recent GOCE geopotential models in BrazilSeveral global geopotential models based on Gravity field and steady-state Ocean Circulation Explorer (GOCE) data have been published in the last two years. Some of these models use combinations of different satellite missions, while others use only GOCE data. This paper presents the evaluation and analysis of each approach using GOCE data in the Southeast of Brazil. Two assessments have been made. We compared the geoid heights derived from GOCE-based models with the geoidal heights from 176 GPS stations on leveling benchmarks. The findings show an improvement in GOCE-based models TIM_R3 (0.40 m) and DIR_R3 (0.39 m) for degree and order 210 in relation to EGM2008 (0.44 m) in terms of RMS. For the other models the results did not exceed 0.44 m. The second evaluation reports the comparison in terms of gravity disturbances between terrestrial gravity data and the models. The results, in terms of RMS and up to degree and order 210, indicate slightly low GOCO 02S values (10.34 mGal), TIM_R2 (10.37 mGal) and TIM_R3 (10.47 mGal) compared to EGM2008 (10.66 mGal). We also applied the residual terrain model and, as a result, the RMS errors were reduced by ~35% (~6.0 mGal) in the entire area and by ~45% in the mountain region.

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.

Spatial Error Metrics for Oceanographic Model Verification

2012 ◽  
Vol 29 (2) ◽  
pp. 260-266 ◽  
Author(s):  
Sean B. Ziegeler ◽  
James D. Dykes ◽  
Jay F. Shriver
Keyword(s):  
Least Squares ◽  
Ocean Circulation ◽  
Displacement Component ◽  
Ocean Model ◽  
Model Verification ◽  
Temperature Fields ◽  
Spatial Error ◽  
Error Metrics ◽  
Study Results ◽  
Oceanographic Model

Abstract A common problem with modern numerical oceanographic models is spatial displacement, including misplacement and misshapenness of ocean circulation features. Traditional error metrics, such as least squares methods, are ineffective in many such cases; for example, only small errors in the location of a frontal pattern are translated to large differences in least squares of intensities. Such problems are common in meteorological forecast verification as well, so the application of spatial error metrics have been a recently popular topic there. Spatial error metrics separate model error into a displacement component and an intensity component, providing a more reliable assessment of model biases and a more descriptive portrayal of numerical model prediction skill. The application of spatial error metrics to oceanographic models has been sparse, and further advances for both meteorology and oceanography exist in the medical imaging field. These advances are presented, along with modifications necessary for oceanographic model output. Standard methods and options for those methods in the literature are explored, and where the best arrangements of options are unclear, comparison studies are conducted. These trials require the reproduction of synthetic displacements in conjunction with synthetic intensity perturbations across 480 Navy Coastal Ocean Model (NCOM) temperature fields from various regions of the globe throughout 2009. Study results revealed the success of certain approaches novel to both meteorology and oceanography, including B-spline transforms and mutual information. That, combined with other common methods, such as quasi-Newton optimization and land masking, could best recover the synthetic displacements under various synthetic intensity changes.

Using gravity gradients to estimate fault parameters in the Wichita Uplift region

2020 ◽  
Vol 222 (3) ◽  
pp. 1704-1716
Author(s):  
Sibel Uzun ◽  
Kamil Erkan ◽  
Christopher Jekeli
Keyword(s):  
Gravity Gradient ◽  
Gravity Gradients ◽  
Strong Constraint ◽  
North American Continent ◽  
The North ◽  
Field Curvature ◽  
Fault Parameters ◽  
Gravitational Gradients ◽  
Southern Oklahoma ◽  
Dip Angle

SUMMARY The geological setting of southwestern Oklahoma and northeastern Texas is an ideal example of an aulacogen, the result of the tectonic evolution of a failed rift of the North American continent during the Palaeozoic era (540–360 Ma). The Wichita Province forms the uplifted basement portion of this Southern Oklahoma Aulacogen (SOA). The major fault zones to its north and south are clearly evident in gravity gradient maps produced by the recently constructed Earth Gravitational Model 2008 (EGM2008). Fault parameters, such as the dip angle, location and density contrasts have been estimated from profiles of seismic data and local gravimetry in the 1990s. On the other hand, gravitational gradients that are derived from EGM2008 and then combined to form the differential field curvature are particularly indicative of linear structures such as dip-slip faults. They are used here exclusively, that is, without additional geophysical constraints, in an optimal, least-squares estimation based on the Monte Carlo technique of simulated annealing to determine dip angle and location parameters of the major faults that border the Wichita Uplift region. Results show that these faults have small dip angles, in basic agreement with the low-angle faults inferred from seismic studies. The EGM2008 gradients also appear in some cases to provide an improved map of the major faults in the region, thus offering a strong constraint on their location.

scholarly journals An Improved Model of the Earth’s Static Gravity Field Solely Derived from Reprocessed GOCE Data

2021 ◽  
Author(s):  
Jan Martin Brockmann ◽  
Till Schubert ◽  
Wolf-Dieter Schuh
Keyword(s):  
Gravity Field ◽  
Ocean Circulation ◽  
Gravity Anomalies ◽  
Geoid Height ◽  
Gravity Gradients ◽  
Data Set ◽  
Gravity Field Recovery ◽  
Global Gravity ◽  
The Impact ◽  
Goce Satellite

AbstractAfter it was found that the gravity gradients observed by the Gravity field and steady-state Ocean Circulation Explorer (GOCE) satellite could be significantly improved by an advanced calibration, a reprocessing project for the entire mission data set was initiated by ESA and performed by the GOCE High-level processing facility (GOCE HPF). One part of the activity was delivering the gravity field solutions, where the improved level 1b and level 2 data serve as an input for global gravity field recovery. One well-established approach for the analysis of GOCE observations is the so-called time-wise approach. Basic characteristics of the GOCE time-wise solutions is that only GOCE observations are included to remain independent of any other gravity field observables and that emphasis is put on the stochastic modeling of the observations’ uncertainties. As a consequence, the time-wise solutions provide a GOCE-only model and a realistic uncertainty description of the model in terms of the full covariance matrix of the model coefficients. Within this contribution, we review the GOCE time-wise approach and discuss the impact of the improved data and modeling applied in the computation of the new GO_CONS_EGM_TIM_RL06 solution. The model reflects the Earth’s static gravity field as observed by the GOCE satellite during its operation. As nearly all global gravity field models, it is represented as a spherical harmonic expansion, with maximum degree 300. The characteristics of the model and the contributing data are presented, and the internal consistency is demonstrated. The updated solution nicely meets the official GOCE mission requirements with a global mean accuracy of about 2 cm in terms of geoid height and 0.6 mGal in terms of gravity anomalies at ESA’s target spatial resolution of 100 km. Compared to its RL05 predecessor, three kinds of improvements are shown, i.e., (1) the mean global accuracy increases by 10–25%, (2) a more realistic uncertainty description and (3) a local reduction of systematic errors in the order of centimeters.

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