Steady-state Ocean Circulation Explorer Research Articles

FIR, IIR and Wavelet Algorithms for the Rigorous Filtering of GOCE SGG Data to the GOCE MBW

Gravity field and steady-state Ocean Circulation Explorer (GOCE) data are strongly affected by noise and long-wavelength errors outside the satellite measurement bandwidth (MBW). One of the main goals in utilizing GOCE data for gravity field modeling is the application of filtering techniques that can remove gross errors and reduce low-frequency errors and high-frequency noise while preserving the original signal. This paper aims to present and analyze three filtering strategies used to de-noise the GOCE Level 2 data from long-wavelength correlated errors and noise. These strategies are Finite Impulse Response (FIR), Infinite Impulse Response (IIR), and Wavelet Multi-resolution Analysis (WL), which have been applied to GOCE residual second order derivatives of the gravity potential. Several experiments were performed for each filtering scheme in order to identify the ideal filtering parameters. The outcomes indicate that all the suggested filtering strategies proved to be effective in removing low-frequency errors while preserving the signals in the GOCE MBW, with FIR filtering providing the overall best results.

Spectrally Consistent Mean Dynamic Topography by Combining Mean Sea Surface and Global Geopotential Model Through a Least Squares-Based Approach

The filtering procedure is usually mandatory for modeling mean dynamic topography (MDT) when a geodetic approach based on the Mean Sea Surface (MSS) and the Global Geopotential Model (GGM) is used. This is due to the inconsistent spectral contents between MSS and GGM. However, traditional isotropic filtering algorithms (e.g., Gaussian filter) consider neither the MDT locations nor their azimuth when smoothing the signal within the filtering radius. Hence, the isotropic filtering will attenuate the MDT signal near the current and filter the current signal into the surrounding ocean, which may lead to signal contamination and distortion. In this study, we set up a least squares-based (LS) approach to model MDT signal from the altimeter-derived MSS and geoid height using spherical harmonics from GGMs, where MDT is parameterized by Lagrange Basis Functions (LBFs). The design matrix is segmentally established, considering the error information of GGM in various spectral bands. Numerical experiments in the Gulf Stream show that applications of full error variance-covariance matrix or only diagonal error variance of GGM may have marginal effects on the MDT modeling. The MDT computed from this LS-based approach using the latest releases of Gravity Field and Steady-state Ocean Circulation Explorer (GOCE) geoid models, i.e., GO_CONS_GCF_2_DIR_R6 and Gravity Observation Combination 06s model (GOCO06s), have the best agreement with the comparison data, especially near the current region. Deduced geostrophic velocities based on the MDT solutions show that the LS-based approach recovers the current signal better than the Gaussian filtering by 1.8 cm/s. Estimated error map illustrates that errors are more concentrated near the coastal region.

Piecewise acceleration orbital modeling: a GOCE satellite case study

In this work, the Precise Science Orbit (PSO) of the Gravity Field and Steady-State Ocean Circulation Explorer Mission (GOCE) satellite, acquired via the European Space Agency, served as the reference orbit for the testing various variants of the GOCE satellite orbit modeling. The GOCE satellite positions along the reduced-dynamic PSO orbit were treated as pseudo-observations in the satellite orbit improvement process in the least squares sense. This process was realized using dedicated extended Toruń Orbit Processor software which enabled determining corrections to the orbital initial conditions and the set of parameters, necessary to determine additional empirical accelerations of the satellite in the radial-track, along-track and cross-track directions. These piecewise accelerations were determined in successive equal intervals (pieces) into which the processed orbital arcs were divided. For modeling the accelerations, polynomials of different degrees were used. The obtained RMS differences between the improved orbits and the reference PSO orbit were determined for various orbital arc lengths up to 1-day. The best RMS of the fits for the 1-day arcs was in the range from 2.0 to 3.2 mm with significantly worst results for along-track direction. Based on the set of solutions determined, the number of orbital parameters for adopted accuracy thresholds and the upper limit of their number, that can be estimated depending on the length of the orbital arc, under given numerical conditions were obtained. The optimal form of the polynomial modeling of the estimated accelerations also depends partly on the length of the processed orbital arc. For shorter arcs (45 min and less), the second- third- and fourth-order polynomial gives the best results, while for longer arcs (90, 180, 360, 720 and 1440 min), zero- and first-degree polynomials are the most effective. A very promising solution with the RMS of the fit of 0.1 mm for a 1-min arc using the fourth-order polynomial was obtained in a perspective of the future use of the short arc approach to the fit of 1-day arcs. Additionally, solution variants with non-equal numbers of orbital pieces for the radial-along-and cross-track directions were obtained. In the case of the solution for an arc length of 1-day, the distribution of residuals and their statistics in the aforementioned radial-, along-and cross-track directions are presented.

Development of the Korean National Geoid Model (KNGeoid18) and Applications for the Height Determination of Coastal Land Points

Lee, J.; Kwon, J.H.; Lee, Y., and Lee, H., 2021. Development of the Korean National Geoid Model (KNGeoid18) and applications for the height determination of coastal land points. In: Lee, J.L.; Suh, K.-S.; Lee, B.; Shin, S., and Lee, J. (eds.), Crisis and Integrated Management for Coastal and Marine Safety. Journal of Coastal Research, Special Issue No. 114, pp. 405–409. Coconut Creek (Florida), ISSN 0749-0208. Since 2008, new land gravity data showing a homogeneous distribution and high precision have been obtained in Korea. In addition, a new version of the global geopotential models which were developed based on observations by the Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) satellite are available. Thus, a gravimetric geoid was newly developed by the “Remove-Restore” technique using the experimental gravity field model 2016 (XGM2016) and more than 12,000 points of land gravity data. In addition, airborne, shipborne, and Danish Technical University 2010 (DTU10) altimeter gravity data, as well as a terrain model, were applied for geoid modeling. As a final product of the study, the hybrid geoid, Korean National Geoid model 2018 (KNGeoid18), was modeled by fitting the gravimetric geoid to a total of 2,791 points of global navigation satellite system (GNSS)/leveling data located over the entire Korean peninsula. The degree of fit of KNGeoid18 was calculated to be approximately 2.3 cm. One of the necessities of a local geoid model is to efficiently determine the orthometric height in terms of time and cost. Thus, GNSS surveying was conducted at 19 points and GNSS-derived orthometric heights were computed. Among the 19 points, the precision of the official orthometric heights at 12 points located in mountainous areas is known to be larger than 10 cm; hence, the GNSS-derived orthometric heights were calculated using Trimble business center (TBC), Leica geo-office (LGO), and Giodis, and compared with each other. As a result, it was found that the difference in heights at 12 points did not exceed 5 cm. The other 9 points, located in coastal areas, had a difference smaller than 3 cm compared to the official orthometric height. It is expected that orthometric heights with a target precision of 3–5 cm would be determined by GNSS surveying and the local geoid model, but an improvement of the geoid model in mountainous areas is still necessary.

Gravimetry and petrophysics for defining the intracratonic and rift basins of the Western-Central Africa zone

The global gravity field obtained from the observations of the satellite Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) satellite offers new opportunities in defining density variations of earth’s crust and mantle, allowing new insights into the structure of specific geologic features. The Central African Rift is a key feature in understanding the dismemberment of Gondwana, and we contribute to defining the crustal density structure underlying the rift. The presence of a narrow and up to 12 km deep basin implies crustal stretching allowed the sediment to accumulate, but a key question is whether the stretching processes also affected the deeper layers of the crust or was limited to the upper crust. The study area includes a subbasin of the greater Chad sag basin, which extends over 1500 × 1500 km and occupies the center of North-Central Africa, shared between the countries of Chad, Sudan, Nigeria, Niger, Algeria, Libya, and Cameroon. We find that the rifting affected the lower crust of the West African Rift, and we evaluate evidence for a 1500 km long and several km thick magmatic crustal intrusion presumably associated with underplating and crustal thinning. We estimate that the stretching factor must be at least 1.5 and had affected the entire crust. To our knowledge, the identification of a continuous body of magmatic intrusions is new and has been only possible through the recent global gravity field. The magmatism has altered the thermal conditions from the time of emplacement on, and it is relevant for the maturation of hydrocarbons present in the sediments. The timing of the magmatism is presumably tied to two pulses of volcanism documented in the rift, associated with the first postrift phase from 96 to 88 Ma and the second postrift phase from 23 Ma up to the Quaternary.

Reconstruction Method of Satellite Gravity Gradient Measurement Angular Velocity by Combining Star Tracker Quaternion

Objectives In order to calculate the high precision gravity gradient in level 1b (L1b) data processing of gravity field and steady-state ocean circulation explorer(GOCE)satellite, it is necessary to accurately measure the satellite attitude angular velocity. In the coordinate system transformation of the attitude data of astrology, the low precision angular velocity components of a single astrology instrument will transmit the noise to other angular velocity components, which will affect the calculation accuracy of the whole gravity gradient. Methods In this paper, based on the noise characteristics of the astrological instrument, the weighted matrix of the noise distribution on each axis of the astrological instrument is constructed, and the optimal attitude quaternion is solved jointly for the attitude quaternion of two or more astrological instruments, so as to provide accurate attitude control for subsequent angular velocity recovery. Results Compared with the single astro-meter calculation method, the accuracy of the optimal attitude angular velocity components wy and wz obtained by the combination of multiple astro-meters can reach about 1 order of magnitude higher within 10-100 mHz, and the noise level is up to 10-6 rad/s, which can effectively suppress the noise propagation caused by the low precision angular velocity components in coordinate system transformation. Conclusions The results show that the satellite attitude angular velocity calculated by the combination of multiple astrological instruments can be significantly improved in the whole power spectral density, the power spectral density of gravity gradient trace values calculated by the combined method of multiple astrologers is also significantly improved compared with the single astrologer method.

The Solar Eclipse Effects on the Upper Thermosphere

AbstractTheoretical studies have shown that the solar eclipse can have significant impacts on the thermospheric mass density, which, however, has not been confirmed from the observational perspective. In this study, we present direct observations of the thermospheric density responses to three solar eclipses based on the measurements of Gravity Recovery and Climate Experiment (GRACE) and Gravity field and steady state Ocean Circulation Explorer (GOCE). It was observed that the eclipses induced about 20% and 25% density depletions at GRACE altitudes (360 and 480 km, respectively) and about 10% depletions at GOCE altitudes (∼270 km). Moreover, the eclipse could generate large‐scale traveling atmospheric disturbances (TADs), which propagate globally even from the duskside to the dawnside after the eclipse ended. Those thermospheric responses could be generally reproduced by Thermosphere Ionosphere Electrodynamics General Circulation Model (TIEGCM). However, the simulated densities recover more rapidly than the observations at the duskside. This study provides observational evidence to validate the results from theoretical models and further bring insights into the mechanism of eclipse effects on the ionosphere‐thermosphere system.

Mean Dynamic Topography Modeling Based on Optimal Interpolation from Satellite Gravimetry and Altimetry Data

Mean dynamic topography (MDT) is crucial for research in oceanography and climatology. The optimal interpolation method (OIM) is applied to MDT modeling, where the error variance–covariance information of the observations is established. The global geopotential model (GGM) derived from GOCE (Gravity Field and Steady-State Ocean Circulation Explorer) gravity data and the mean sea surface model derived from satellite altimetry data are combined to construct MDT. Numerical experiments in the Kuroshio over Japan show that the use of recently released GOCE-derived GGM derives a better MDT compared to the previous models. The MDT solution computed based on the sixth-generation model illustrates a lower level of root mean square error (77.0 mm) compared with the ocean reanalysis data, which is 2.4 mm (5.4 mm) smaller than that derived from the fifth-generation (fourth-generation) model. This illustrates that the accumulation of GOCE data and updated data preprocessing methods can be beneficial for MDT recovery. Moreover, the results show that the OIM outperforms the Gaussian filtering approach, where the geostrophic velocity derived from the OIM method has a smaller misfit against the buoy data, by a magnitude of 10 mm/s (17 mm/s) when the zonal (meridional) component is validated. This is mainly due to the error information of input data being used in the optimal interpolation method, which may obtain more reasonable weights of observations than the Gaussian filtering method.

Gravity Field Recovery and Error Analysis for the MOCASS Mission Proposal Based on Cold Atom Interferometry

Satellite missions providing data for a continuous monitoring of the Earth gravity field and its changes are fundamental to study climate changes, hydrology, sea level changes, and solid Earth phenomena. GRACE-FO (Gravity Recovery and Climate Experiment Follow-On) mission was launched in 2018 and NGGM (Next Generation Gravity Mission) studies are ongoing for the long-term monitoring of the time-variable gravity field. In recent years, an innovative mission concept for gravity measurements has also emerged, exploiting a spaceborne gravity gradio-meter based on cold atom interferometers. In particular, a team of researchers from Italian universities and research institutions has proposed a mission concept called MOCASS (Mass Observation with Cold Atom Sensors in Space) and conducted the study to investigate the performance of a cold atom gradiometer on board a low Earth orbiter and its impact on the modeling of different geophysical phenomena. This paper presents the analysis of the gravity gradient data attainable by such a mission. Firstly, the mathematical model for the MOCASS data processing will be described. Then numerical simulations will be presented, considering different satellite orbital altitudes, pointing modes and instrument configurations (single-arm and double-arm); overall, data were simulated for twenty different observation scenarios. Finally, the simulation results will be illustrated, showing the applicability of the proposed concept and the improvement in modeling the static gravity field with respect to GOCE (Gravity Field and Steady-State Ocean Circulation Explorer).

Joint inversion of ground gravity data and satellite gravity gradients between Nepal and Bhutan: New insights on structural and seismic segmentation of the Himalayan arc

Along-strike variation in the geometry of lithospheric structures is a key control parameter for the occurrence and propagation of major interplate earthquakes in subduction and collision zones. The lateral segmentation of the Himalayan arc is now well-established from various observations, including topography, gravity anomalies, exhumation rates, and present-day seismic activity. Good knowledge of the main geometric features of these segments and their boundaries is thus the next step to improve seismic hazard assessment in this area. Following recent studies, we focus our approach on the transition zone between Nepal and Bhutan where both M > 8 earthquakes and changes in the geometry of the Indian plate have been documented. Ground gravity data sets are combined with satellite gravity gradients provided by the GOCE mission (Gravity Field and Steady-State Ocean Circulation Explorer) in a joint inversion to assess the location and the geometry of this transition. We obtain a ca. 10 km wide transition zone located at the western border of Bhutan that is aligned with the Madhupur fault in the foreland and coincides with the Dhubri–Chungthang fault zone and the Yadong-Gulu rift in Himalaya and southern Tibet, respectively. This sharp segment boundary at depth can act as a barrier to earthquake rupture propagation. It can possibly restrict the size of large earthquakes and thus reduce the occurrence probability of M > 9 earthquakes along the Main Himalayan Thrust.

The construction of high precision geostrophic currents based on new gravity models of GOCE and satellite altimetry data

The new gravity field models of gravity field and steady-state ocean circulation explorer (GOCE), TIM_R6 and DIR_R6, were released by the European Space Agency (ESA) in June 2019. The sixth generation of gravity models have the highest possible signal and lowest error levels compared with other GOCE-only gravity models, and the accuracy is significantly improved. This is an opportunity to build high precision geostrophic currents. The mean dynamic topography and geostrophic currents have been calculated by the 5th (TIM_R5 and DIR_R5), 6th (TIM_R6 and DIR_R6) release of GOCE gravity field models and ITSG-Grace2018 of GRACE gravity field model in this study. By comparison with the drifter results, the optimal filtering lengths of them have been obtained (for DIR_R5, DIR_R6, TIM_R5 and TIM_R6 models are 1° and for ITSG-Grace2018 model is 1.1°). The filtered results show that the geostrophic currents obtained by the GOCE gravity field models can better reflect detailed characteristics of ocean currents. The total geostrophic speed based on the TIM_R6 model is similar to the result of the DIR_R6 model with standard deviation (STD) of 0.320 m/s and 0.321 m/s, respectively. The STD of the total velocities are 0.333 m/s and 0.325 m/s for DIR_R5 and TIM_R5. When compared with ITSG-Grace2018 results, the STD (0.344 m/s) of total geostrophic speeds is larger than GOCE results, and the accuracy of geostrophic currents obtained by ITSG-Grace2018 is lower. And the absolute errors are mainly distributed in the areas with faster speeds, such as the Antarctic circumpolar circulation, equatorial region, Kuroshio and Gulf Stream areas. After the remove-restore technique was applied to TIM_R6 MDT, the STD of total geostrophic speeds dropped to 0.162 m/s.

Quantifying the individual contributions of GOCE gradients for regional quasi-geoid modeling in a relatively rough topography

Gravity field and steady-state Ocean Circulation Explorer (GOCE) is the first satellite mission that measures the gravity gradients (GGs) in space with primary objective of determining the gravity field of the Earth with maximum spatial resolution and accuracy. GOCE GGs have been used for the computation of global gravity field models (GGMs) represented by the surface spherical harmonics for about 10 years. However, they may potentially improve the regional quasi-geoid solutions computed from terrestrial gravity and a Global Geopotential Model (GGM) particularly in mountainous areas with rough gravity field. This study exploits the full signal content in the GOCE Level-2 GGs given in Local North-Oriented Frame for improved regional quasi-geoid modeling in Auvergne test area located in France. The least squares collocation method is used in single-input and single-output (SISO) mode where the input is the residual terrestrial gravity data corrected for GGM contribution and residual terrain modeling effects, and also in multiple-input and single-output mode (MISO) where the terrestrial data input is augmented with the four precise GOCE GGs or their combinations. The single outputs for both modes are the quasi-geoid heights at 75 GPS collocated leveling benchmarks distributed in the central area and at 7857 Digital Elevation Model (DEM) points covering the whole area. The combination of the terrestrial gravity with the GOCE along-track gradient, having a lower noise level than the others, gives the best results when a single gradient is used. The further incorporation of the off-diagonal gradient to the along-track gradient results in the best MISO solution showing improvements with respect to the SISO solution only at GPS/leveling benchmarks near a large data gap. Intercomparison of the best MISO and SISO solutions at the DEM points suggests substantial quasi-geoid differences up to 13.6 cm in areas of sparse or no gravity data near the Alps where these results could not be assessed due to the lack of GPS-leveling data.

Megathrust Slip Behavior for Great Earthquakes Along the Sumatra-Andaman Subduction Zone Mapped From Satellite GOCE Gravity Field Derivatives

During the last two decades, space geodesy allowed mapping accurately rupture areas, slip distribution, and seismic coupling by obtaining refined inversion models and greatly improving the study of great megathrust earthquakes. A better understanding of these phenomena involving large areas of hundreds of square kilometers came from the last gravity satellite mission that allowed detecting mass transfer through the Earth interior. In this work, we performed direct modeling of satellite GOCE (Gravity Field and Steady-State Ocean Circulation Explorer) derived gravity gradients up to degree/order N = 200 of the harmonic expansion and then corrected this by the effect of topography. Cutting off the model up to this degree/order allows inferring mass heterogeneities located at an approximate depth of 31 km, just along the plate interface where most (but not all) significant slip occurs. Then, we compared the vertical gravity gradient to well-constrained coseismic slip models for three of the last major earthquakes along the Sunda interface. We analyzed seismic rupture behavior for recent and for historical earthquakes along this subduction margin and the relationship of the degree of interseismic coupling using the gravity signal. From this, we found that strong slip patches occurred along minima gravity gradient lobes and that the maximum vertical displacements were related quantitatively to the gravity-derived signal. The degree of interseismic coupling also presents a good correspondence to the vertical gravity gradient, showing an inverse relationship, with low degrees of coupling over regions of relatively higher density. This along-strike segmentation of the gravity signal agrees with the along-strike seismic segmentation observed from recent and historical earthquakes. The thermally controlled down-dip ending of the locked fault zone along central Sumatra also presented an inverse relationship with the density structure along the forearc inferred using our modeling. From this work, we inferred different mass heterogeneities related to persistent tectonic features along the megathrust and along the marine forearc, which may control strain accumulation and release along the megathrust. Combining these data with geodetical and seismological data could possibly delimit and monitor areas with a higher potential seismic hazard around the world.

The earth\u2019s gravity field recovery using the third invariant of the gravity gradient tensor from GOCE

Due to the independence of the gradiometer instrument’s orientation in space, the second invariant I_2 of gravity gradients in combination with individual gravity gradients are demonstrated to be valid for gravity field determination. In this contribution, we develop a novel gravity field model named I3GG, which is built mainly based on three novel elements: (1) proposing to utilize the third invariant I_3 of the gravity field and steady-state ocean circulation explorer (GOCE) gravity gradient tensor, instead of using the I_2, similar to the previous studies; (2) applying an alternative two-dimensional fast fourier transform (2D FFT) method; (3) showing the advantages of I_3 over I_2 in the effect of measurement noise from the theoretical and practical computations. For the purpose of implementing the linearization of the third invariant, this study employs the theory of boundary value problems with sphere approximation at an accuracy level of O(J_2^2cdot T_{ij}). In order to efficiently solve the boundary value problems, we proposed an alternative method of 2D FFT, which uses the coherent sampling theory to obtain the relationship between the 2D FFT and the third invariant measurements and uses the pseudo-inverse via QR factorization to transform the 2D Fourier coefficients to spherical harmonic ones. Based on the GOCE gravity gradient data of the nominal mission phase, a novel global gravity field model (I3GG) is derived up to maximum degree/order 240, corresponding to a spatial resolution of 83 km at the equator. Moreover, in order to investigate the differences of gravity field determination between I_3 with I_2, we applied the same processing strategy on the second invariant measurements of the GOCE mission and we obtained another gravity field model (I2GG) with a maximum degree of 220, which is 20 degrees lower than that of I3GG. The root-mean-square (RMS) values of geoid differences indicates that the effects of measurement noise of I3GG is about 20% lower than that on I2GG when compared to the gravity field model EGM2008 (Earth Gravitational Model 2008) or EIGEN-5C (EIGEN: European Improved Gravity model of the Earth by New techniques). Then the accuracy of I3GG is evaluated independently by comparison the RMS differences between Global Navigation Satellite System (GNSS)/leveling data and the model-derived geoid heights. Meanwhile, the re-calibrated GOCE data released in 2018 is also dealt with and the corresponding result also shows the similar characteristics.

GOCO06s – a satellite-only global gravity field model

Abstract. GOCO06s is the latest satellite-only global gravity field model computed by the GOCO (Gravity Observation Combination) project. It is based on over a billion observations acquired over 15 years from 19 satellites with different complementary observation principles. This combination of different measurement techniques is key in providing consistently high accuracy and best possible spatial resolution of the Earth's gravity field. The motivation for the new release was the availability of reprocessed observation data for the Gravity Recovery and Climate Experiment (GRACE) and Gravity field and steady-state Ocean Circulation Explorer (GOCE), updated background models, and substantial improvements in the processing chains of the individual contributions. Due to the long observation period, the model consists not only of a static gravity field, but comprises additionally modeled temporal variations. These are represented by time-variable spherical harmonic coefficients, using a deterministic model for a regularized trend and annual oscillation. The main focus within the GOCO combination process is on the proper handling of the stochastic behavior of the input data. Appropriate noise modeling for the observations used results in realistic accuracy information for the derived gravity field solution. This accuracy information, represented by the full variance–covariance matrix, is extremely useful for further combination with, for example, terrestrial gravity data and is published together with the solution. The primary model data consisting of potential coefficients representing Earth's static gravity field, together with secular and annual variations, are available on the International Centre for Global Earth Models (http://icgem.gfz-potsdam.de/, last access: 11 June 2020). This data set is identified with the following DOI: https://doi.org/10.5880/ICGEM.2019.002 (Kvas et al., 2019b). Supplementary material consisting of the full variance–covariance matrix of the static potential coefficients and estimated co-seismic mass changes is available at https://ifg.tugraz.at/GOCO (last access: 11 June 2020).

Roles of thermospheric neutral wind and equatorial electrojet in pre-reversal enhancement, deduced from observations in Southeast Asia

Previous studies have proposed that both the thermospheric neutral wind and the equatorial electrojet (EEJ) near sunset play important roles in the pre-reversal enhancement (PRE) mechanism. In this study, we have used observations made in the equatorial region of Southeast Asia during March–April and September–October in 2010–2013 to investigate influences of the eastward neutral wind and the EEJ on the PRE’s strength. Our analysis employs data collected by the Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) satellite to determine the zonal (east-west direction) neutral wind at an altitude of ~250 km (bottomside F region) at longitudes of 90°–130°E in the dusk sector. Three ionosondes, at Chumphon (dip lat.: 3.0°N) in Thailand, at Bac Lieu (dip lat.: 1.7°N) in Vietnam, and at Cebu (dip lat.: 3.0°N) in Philippines, provided the data we have used to derive the PRE strength. Data from two magnetometers — at Phuket (dip lat.: 0.1°S) in Thailand and at Kototabang (dip lat.: 10.3°S) in Indonesia — were used to estimate the EEJ strength. Our study is focused particularly on days with magnetically quiet conditions. We have found that the eastward neutral wind and the EEJ are both closely correlated with the PRE; their cross-correlation coefficients with it are, respectively, 0.42 and 0.47. Their relationship with each other is weaker: the cross-correlation coefficient between the eastward neutral wind and the EEJ is just 0.26. Our findings suggest that both the eastward neutral wind and the EEJ near sunset are involved in the PRE mechanism. Based on the weak relationship between these two parameters, however, they appear to be significantly independent of each other. Thus, the wind and the EEJ are likely to be influencing the PRE magnitude independently, their effects balancing each other.

Analysis of limitations on recovery of gravity field based on satellite gravity gradient data

Although satellite gravity gradient data plays a great role in determining short-wavelength part of static gravity field model, accuracy of the long-wavelength part of gravity field model recovered by them are poor, which leads to only a few applications in time-variable gravity investigation. The reason is that some factors limit the accuracy of the gravity field recovered using gradient data, including accuracy of the gravity gradient observations, measurement bandwidth (MBW) of gradiometer, satellite inclination, etc. This paper aims at analyzing the influence of these limitations on gravity field recovery and discusses the possibility of time-variable gravity field detection by using gravity gradient observations. Firstly, for arbitrary satellite orbit inclination, we give the frequency distributions of all the components of gravity gradients (i.e. Txx,Tyy,Tzz,Txy,TxzandTyz, ). The results show that the maximum frequency of each component of the gravity gradients is the same, i.e. l/Ts (l is degree of the gravity field model, Ts is the orbital periods), and it is not influenced by the inclination of the satellite orbits. Secondly, the paper gives a theory proof to explain why only the low orders of the coefficients are influenced by polar gaps. Big polar gaps are experimented by a numerical test with inclination of 45°. Finally, considering that the measurement bandwidth can be expanded and accuracy of gradient observations can be improved by superconducting gravity gradiometer (SGG) compared to gradiometer used in Gravity field and steady-state Ocean Circulation Explorer (GOCE), the possibility of detecting time-variable gravity using gravity gradient observations is discussed. The results show that the SGG creates errors in MBW with magnitude of 0.014 mE, which is smaller than the magnitude of the time-variable gravity gradient signals (i.e., 0.02 mE) derived from Gravity Recovery and Climate Experiment (GRACE) gravity field models. This indicates the potential of SGG in time-variable gravity detection.

Temporal Gravity Signals in Reprocessed GOCE Gravitational Gradients

The reprocessing of the satellite gravitational gradiometry (SGG) data from the Gravity field and steady-state Ocean Circulation Explorer (GOCE) satellite mission in 2018/2019 considerably reduced the low-frequency noise in the data, leading to reduced noise amplitudes in derived gravity field models at large spatial scales, at which temporal variations of the Earth’s gravity field have their highest amplitudes. This is the motivation to test the reprocessed GOCE SGG data for their ability to resolve time-variable gravity signals. For the gravity field processing, we apply and compare a spherical harmonics (SH) approach and a mass concentration (mascon) approach. Although their global signal-to-noise ratio is <1, SH GOCE SGG-only models resolve the strong regional signals of glacier melting in Greenland and Antarctica, and the 2011 moment magnitude 9.0 earthquake in Japan, providing an estimation of gravity variations independent of Gravity Recovery and Climate Experiment (GRACE) data. The benefit of combined GRACE/GOCE SGG models is evaluated based on the ice mass trend signals in Greenland and Antarctica. While no signal contribution from GOCE SGG data additional to the GRACE models could be observed, we show that the incorporation of GOCE SGG data numerically stabilizes the related normal equation systems.

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

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.

On the Feasibility of Orbit Determination From Gravity Gradient Invariants

The capability of full-tensor gravity gradients for spacecraft orbit determination has been demonstrated in recent studies. The advantages lie in its independence from ground-based systems and its immunity against spoofing attacks. A common practice is to use Earth rotation parameters and star sensor measurements to isolate the orientation contributions to gravity gradients, which implies that the orbit determination accuracy is affected by the quality of attitude data. This article investigates the feasibility of orbit determination using gravity gradient invariants instead of full-tensor gravity gradients in order to eliminate the necessity of attitude information for frame transformation. The orbit observability is first partially explained by formulating the geometric relationship between orbital elements and geocentric distance and latitude, the latter of which can be obtained from gravity gradient invariants. Then a covariance analysis technique based on the computation of a posterior Cramér–Rao lower bound is developed to assess the orbit determination accuracy. It is assumed that the gravity gradient biases due to bandwidth limitation have been calibrated. Simulations are carried out to analyze the effects of sampling rate, orbital inclination, orbital height, and gradiometer noise level. Results show that orbit determination from gravity gradient invariants has better position accuracy in the radial direction but has degraded accuracies in the along-track and cross-track directions compared to orbit determination using full-tensor gravity gradients. The covariance analysis technique is applied to real flight data from gravity field and steady-state ocean circulation explorer. Radial, along-track, and cross-track position accuracies of 1.8, 78, and 255 m have been achieved. Future study will deal with biases in actual measurements to fulfill real orbit determination.