Steady-state Ocean Circulation Explorer Research Articles

Third‐Order Structure Functions of Zonal Winds in the Thermosphere Using CHAMP and GOCE Observations

AbstractWe use multi‐year observations of cross‐track winds (u) from the CHAllenging Minisatellite Payload (CHAMP) and the Gravity Field and Steady State Ocean Circulation Explorer (GOCE) to calculate third‐order structure functions in the thermosphere as a function of horizontal separation (s). They are computed using the mean (〈δu3〉) and the median and implemented over non‐polar satellite paths in both hemispheres. On height averages, 〈δu3〉 is shown to scale with s2 for s ≃ 80–1,000 km, in agreement with equivalent estimates in the lower atmosphere from aircraft observations. Conversely, follows an s3 power law for almost the whole s range, consistent with the two‐dimensional turbulence scaling law for a direct enstrophy cascade. These scaling laws appear independent of winds in distinct atmospheric regions. Furthermore, the functions are predominantly positive, indicating a preferential cyclonic motion for the wind.

Assessment of the Added Value of the GOCE GPS Data on the GRACE Monthly Gravity Field Solutions

The time-varying gravity field models derived from the Gravity Recovery and Climate Experiment (GRACE) satellite mission suffer from pronounced longitudinal stripe errors in the spatial domain. A potential way to mitigate such errors is to combine GRACE data with observations from other sources. In this study, we investigate the impacts on GRACE monthly gravity field solutions of incorporating the GPS data collected by the Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) mission. To that end, we produce GRACE/GOCE combined monthly gravity field solutions through combination on the normal equation level and compare them with the GRACE-only solutions, for which we have considered the state-of-the-art ITSG-Grace2018 solutions. Analysis in the spectral domain reveals that the combined solutions have a notably lower noise level beyond degree 30, with cumulative errors up to degree 96 being reduced by 31%. A comparison of the formal errors reveals that the addition of GOCE GPS data mainly improves (near-) sectorial coefficients and resonant orders, which cannot be well determined by GRACE alone. In the spatial domain, we also observe a significant reduction by at least 30% in the noise of recovered mass changes after incorporating the GOCE GPS data. Furthermore, the signal-to-noise ratios of mass changes over 180 large river basins were improved by 8–20% (dependent on the applied Gaussian filter radius). These results demonstrate that the GOCE GPS data can augment the GRACE monthly gravity field solutions and support a future GOCE-type mission for tracking more accurate time-varying gravity fields.

Evaluation of TIEGCM based on GOCE neutral density

The Thermosphere Ionosphere Electrodynamic General Circulation Model (TIEGCM), as one of the most advanced physical models of the Earth’s thermosphere and ionosphere, is not only widely used in scientific research, but also has essential reference value in aerospace operations. In this study, we use Gravity field and steady-state Ocean Circulation Explorer (GOCE) neutral density to evaluate the accuracy of the TIEGCM. The assessment is performed on both time and spatial scales. The time scales are conducted annually, monthly, and daily, while the spatial scales are carried out in terms of altitude, latitude, and local time. On the time scales, the performance of the TIEGCM on the monthly time scale is better than that on the annual time scale. Also, the performance on the daily time scale is better than that on the monthly time scale. The relative deviation shows a significant seasonal variation, that is, larger in winter and summer and smaller in spring and autumn. In addition, the relative deviation shows a negative correlation with F10.7 and Ap. On the spatial scale, with the increase in altitude, the average relative deviation of the model becomes larger in general. The relative deviation is usually larger at middle latitudes in the Northern Hemisphere and high latitudes in the Southern Hemisphere. Finally, on the scale of local time, the relative deviation changes more dramatically in local morning than at dusk.

The gravitational signature of the dynamics of oceanization in the Gulf of Aden

We perform a new gravity analysis in the Gulf of Aden with the aim of finding new constraints on the geodynamic evolution of the area. Our analysis is developed within the frame of the recent GO_CONS_GCF_2_TIM_R6 global gravity model solution (Brockmann et al., 2021) that reflects the Earth's static gravity field as observed by GOCE (Gravity field and steady-state Ocean Circulation Explorer). We analyzed the solution at different harmonic degrees, to account for different depths and dimensions of the sources. Terrain correction has been performed by means of a spherical tesseroidal methodology (Marotta and Barzaghi, 2017) and the obtained corrected Geodetic Residual Gravitation has been compared to the Model Residual Gravitation predicted by means of a 2D visco-plastic finite element thermo-mechanic model that simulates the dynamics of the Gulf of Aden, from rifting to oceanization. In order to perform the comparison between observed and predicted gravitational features, data have been extracted along five profiles crossing the Gulf of Aden at different sectors, from the south-east to the north west. Via the Model Residual Gravitation we reproduce its geodetic counterpart, obtaining a characteristic hat-shaped pattern, with a central plateau portraying the highest values, flanked by two regions where the residual gravitation diminishes, finally reaching the lowest values at the far continental domains. The maximum variations of the residual gravitation values, from ridge to continental domain, range between 280 and 420 mGal and the steepest decrease occurs over distances of 200 km for the thick crust model and of 100–150 km for the thin crust model. Finally, the comparison between Geodetic and Model Residual Gravitation allows to further constrain the dynamics of the Gulf of Aden oceanization occurring by a slow passive rift of a hot 150 km thick lithosphere characterized by an initial 40 km thick crust.

The Impact of Different Filters on the Gravity Field Recovery Based on the GOCE Gradient Data

The electrostatic gravity gradiometer carried by the Gravity field and steady-state Ocean Circulation Explorer (GOCE) satellite is affected by accelerometer noise and other factors; hence, the observation data present complex error characteristics in the low-frequency domain. The accuracy of the recovered gravity field will be directly affected by the design of the filters based on the error characteristics of the gradient data. In this study, the applicability of various filters to different errors in observation is evaluated, such as the 1/f error and the orbital frequency errors. The experimental results show that the cascade filter (DARMA), which is formed of a differential filter and an autoregressive moving average filter (ARMA) filter, has the best accuracy for the characteristic of the 1/f low-frequency error. The strategy of introducing empirical parameters can reduce the orbital frequency errors, whereas the application of a notch filter will worsen the final solution. Frequent orbit changes and other changes in the observed environment have little impact on the new version gradient data (the data product is coded 0202), while the influence cannot be ignored on the results of the old version data (the data product is coded 0103). The influence can be effectively minimized by shortening the length of the arc. By analyzing the above experimental findings, it can be concluded that the inversion accuracy can be effectively improved by choosing the appropriate filter combination and filter estimation frequency when solving the gravity field model based on the gradient data of the GOCE satellite. This is of reference significance for the updating of the existing models.

Replacement of the part of gravity model and of remaining dynamic models by empirical accelerations in the fit processes of a low-Earth satellite orbit and factors limiting their accuracy

This work contains the results of calculations performed to prove the ability of estimated orbital parameters for the replacement of dynamic models in the orbit determination of a sample low-Earth-orbiting satellite. The obtained solutions include two cases of the absorption of dynamic models. In the first case, the contribution of dynamic models, apart from the gravity field, was absorbed, i.e., the satellite motion was described by the gravity field and estimated parameters. In the second case, the contributions of all dynamic models, including the gravity field, were absorbed. For the gravity field model, the absorption concerned its selected parts. In this case, the satellite motion was modeled only by the gravity model truncated to different degrees and orders and an appropriate set of orbital parameters. In both aforementioned cases, the initial conditions were also improved. Cartesian coordinates of the Gravity Field and Steady-State Ocean Circulation Explorer Mission satellite along selected reference arcs of the official reduced-dynamic orbit served as pseudo-observations in this study. The orbital parameters, also known as empirical accelerations, were determined using the least-squares method by a dedicated orbital package. The results were presented and compared in the form of the root-mean-square (RMS) values of the differences between the estimated orbits and the reference orbits, as well as the corresponding values of the obtained empirical accelerations for selected variants of solutions. The obtained accuracy of the process of the fit of the satellite orbit expressed by the corresponding RMS values, reached a millimeter level. For selected typical solutions, the distribution of residuals and power spectra are presented with an indication of characteristic errors: random and systematic periodic components. Key factors influencing the obtained fit accuracies of estimated orbits are given. Contributions of these factors in the error budget of fits of estimated orbits are also presented. Additionally, in the fit process, the performance of selected gravity models coming from different years is compared to assess the impact of gravity field errors on the results of aforementioned process.

Wave perturbations in Earth’s thermosphere in conjunction with X1.7 solar flare: Observational perspective

Based on satellite observations, the study examines the effect of an X1.7 flare (which occurred on January 27, 2012) on neutral winds and the formation of wave perturbations in Earth’s thermosphere. The Gravity field and steady state Ocean Circulation Explorer (GOCE) observations of the thermospheric zonal wind speed show an increase of 100 m/s in the north polar and 400S to south polar regions on the day side associated with the X1.7 solar flare. This feature is absent for the geomagnetically quiet days in January 2012, when there are no X-class flares. The wave perturbations in thermosphere, derived from the zonal winds are observed to be strongest in the flare day, than in non-flare days, with power index 40. During the flare day, wave perturbation with a wavelength of about 1110 km is dominant and is found preferentially in southern latitudes (above 400S) on the day side. When compared to non-flare days, the TIMED-derived neutral temperature increases by 45 K around the equatorial zone. The measurements also show the substantial temperature gradients over latitude and longitude in the flare situation. This demonstrates the presence of high thermal gradients in the thermosphere caused by the X1.7 solar flare, which causes zonal wind amplification and the launching of strong waves in the thermosphere.

Satellite gradiometry based on a new generation of accelerometers and its potential contribution to Earth gravity field determination

An accurate model of the Earth’s gravity field is beneficial for practical engineering and many applications in geosciences. European Space Agency (ESA) realized the Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) gradiometry mission between 2009 and 2013. However, the low-frequency drift of the onboard electrostatic accelerometers (EA) limits the observation accuracy of the GOCE mission to some extent. Advances in electrostatic and quantum technology offer new measurement concepts for future gradiometry missions. In this study, we evaluate the contributions of several types of accelerometers through numerical closed-loop simulation which rigorously maps the accelerometers’ sensitivities to the gravity field coefficients. In comparison to the simulated results of the GRADIO gradiometer used in GOCE, it is demonstrated that the MicroSTAR-type gradiometer has superior precision within degree and order 100 and provides more signal information in the off-diagonal components of the gravity gradient tensor (GGT). The precision of the gravity field model recovery from a HybridACC-type gradiometer is significantly affected by the noise level of the cold atom interferometry (CAI) accelerometer. A HybridACC-type gradiometer with low CAI performance (1×10-9m·s-2/Hz) only favors the high degree component because of its higher accuracy in the measurement bandwidth (MBW) between 5 mHz and 100 mHz. While a better CAI performance up to 1×10-11m·s-2/Hz will increase retrieval performance remarkably. With an orbital rotation compensation mechanism, the CAI gradiometer performs with greater accuracy overall. Otherwise, the accuracy based on this sort of gradiometer is only superior up to degree 50.

Iterative approaches for regional Moho determination using on-orbit gravity gradients: A case study in Qinghai-Tibet Plateau and its near zone

Summary Moho determination is an important issue in studying the Earth’s interior structure. In accordance with the isostasy-compensation hypothesis in geodesy, it is possible to recover regional or global Moho by employing gravimetric data. The non-linear property is one of the main difficulties in solving the inverse problem of isostasy. To effectively address this issue, we propose an improved iterative inversion method that combines three-dimensional integration and linear regularization to achieve an approximate non-linear solution. To estimate the contributions of different components in the gravity-gradient tensor from the Gravity field and steady-state Ocean Circulation Explorer (GOCE), other than the vertical component, we additionally develop two joint inversion scenarios that utilize diagonal horizontal components and all five non-vertical components. The validating experiments are implemented in Qinghai-Tibet Plateau and its near zone. Simulations and applications illustrate that horizontal responses of Moho undulation are also significant. Yet the off-diagonal components provide minimal contributions, adding only 0.25 km of bias to the joint inversion results. Truncation effects serve as the primary source of systematic errors, resulting in ∼1 km error in vertical inversion results and ∼2.3 km error in joint inversion results. Then, the gravimetric Moho results are compared with CRUST1.0, and they show a generally strong correlation. Differences are obvious at the northern and eastern margins of the plateau. It is maybe due to the local changes in crust-mantle density contrasts. Upwelling of asthenospheric materials and fluid flow in the middle-lower crust are the two main factors. Based on high-precision satellite gravimetry, our study could provide new insights into the tectonic structure of Qinghai-Tibet Plateau.

Reprocessed precise science orbits and gravity field recovery for the entire GOCE mission

ESA’s Gravity field and steady-state Ocean Circulation Explorer (GOCE) orbited the Earth between 2009 and 2013 for the determination of the static part of Earth’s gravity field. The GPS-derived precise science orbits (PSOs) were operationally generated by the Astronomical Institute of the University of Bern (AIUB). Due to a significantly improved understanding of remaining artifacts after the end of the GOCE mission (especially in the GOCE gradiometry data), ESA initiated a reprocessing of the entire GOCE Level 1b data in 2018. In this framework, AIUB was commissioned to recompute the GOCE reduced-dynamic and kinematic PSOs. In this paper, we report on the employed precise orbit determination methods, with a focus on measures undertaken to mitigate ionosphere-induced artifacts in the kinematic orbits and thereof derived gravity field models. With respect to the PSOs computed during the operational phase of GOCE, the reprocessed PSOs show in average a 8–9% better consistency with GPS data, 31% smaller 3-dimensional reduced-dynamic orbit overlaps, an 8% better 3-dimensional consistency between reduced-dynamic and kinematic orbits, and a 3–7% reduction of satellite laser ranging residuals. In the second part of the paper, we present results from GPS-based gravity field determinations that highlight the strong benefit of the GOCE reprocessed kinematic PSOs. Due to the applied data weighting strategy, a substantially improved quality of gravity field coefficients between degree 10 and 40 is achieved, corresponding to a remarkable reduction of ionosphere-induced artifacts along the geomagnetic equator. For a static gravity field solution covering the entire mission period, geoid height differences with respect to a superior inter-satellite ranging solution are markedly reduced (43% in terms of global RMS, compared to previous GOCE GPS-based gravity fields). Furthermore, we demonstrate that the reprocessed GOCE PSOs allow to recover long-wavelength time-variable gravity field signals (up to degree 10), comparable to information derived from GPS data of dedicated satellite missions. To this end, it is essential to take into account the GOCE common-mode accelerometer data in the gravity field recovery.

Coseismic gravitational curvatures changes in a spherical symmetric Earth model

The occurrence of subduction earthquakes usually leads to considerable localized mass migration changes. To improve the detection of earthquake subductions as well as the constraint of fault parameters, we derive expressions that describe changes of the gravitational curvatures (GC), i.e., the third-order derivatives of the Earth's gravitational potential, caused by a point dislocation while adopting a spherical symmetric Earth model. As a 3-D tensor matrix, the GC have twenty-seven components of those seven are independent. First, we investigate the dislocation Love numbers of the Earth's gravitational potential and derive the Green's functions of GC caused by four independent point sources in a spherical inhomogeneous Earth model. We then present the GC changes in a half-space Earth model. Furthermore, we conduct a sensitivity study by using three physical quantities that involve gravitation, gravitational gradients, and GC to compare their abilities in a seismic source depth detection. Our numerical results reveal that changes in the GC are more sensitive to a medium information about the field source compared to gravitation and gravitational gradients. This finding indicates that GC measurements could provide a more detailed information about slip fault parameters when considering a heterogeneous slip. Despite a widespread application of gravity gradients in Earth science, especially after launching the Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) satellite mission, measurements of the third-order derivatives of the gravitational potential have an enormous potential in the study of the solid Earth, although further work is needed in terms of instrument design and development.

GOCE Downward Continuation to the Earth’s Surface and Improvements to Local Geoid Modeling by FFT and LSC

One of the main applications of the gravity field and steady-state Ocean Circulation Explorer (GOCE) satellite data is their combination with local gravity anomalies for geoid and gravity field modeling purposes. The aim of the present paper was the determination of an improved geoid model for the wider Hellenic area, using original GOCE SGG data filtered to retain only useful signals inside the measurement bandwidth (MBW) of the satellite. The filtered SGGs, originally at the satellite altitude, were projected to a mean orbit (MO) and then downward continued to the Earth’s surface (ES) in order to be combined with local gravity anomalies. For the projection to an MO, grids of disturbing gravity gradients from a global geopotential model (GGM) were used, computed per 1 km from the maximum satellite altitude to that of the MO. The downward continuation process was then undertaken using an iterative Monte Carlo (MC) simulated annealing method with GGM gravity anomalies on the ES used as ground truth data. The final geoid model over the wider Hellenic area was estimated, employing the remove–compute–restore method and both Fast Fourier Transform (FFT) and Least Squares Collocation (LSC). Gravity-only, GOCE-only and combined models using local gravity and GOCE data were determined and evaluation of the results was carried out against available GNSS/levelling data in the study area. From the results achieved, it was concluded that even when FFT is used, so that a combined grid of local gravity and GOCE data is used, improvements to the differences regarding GNSS/levelling data by 14.53% to 27.78% can be achieved. The geoid determination with LSC was focused on three different areas over Greece, with different characteristics in the topography and gravity variability. From these results, improvements from 14.73%, for the well-surveyed local data of Thessaly, to 32.88%, over the mountainous area of Pindos, and 57.10% for the island of Crete for 57.10% were found.

Lithospheric Stress Due to Mantle Convection and Mantle Plume over East Africa from GOCE and Seismic Data

The Afar and Ethiopian plateaus are in a dynamic uplift due to the mantle plume, therefore, considering the plume effect is necessary for any geophysical investigation including the estimation of lithospheric stress in this area. The Earth gravity models of the Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) and lithospheric structure models can be applied to estimate the stress tensor inside the Ethiopian lithosphere. To do so, the boundary-value problem of elasticity is solved to derive a general solution for the displacement field in a thin elastic spherical shell representing the lithosphere. After that, general solutions for the elements of the strain tensor are derived from the displacement field, and finally the stress tensor from the strain tensor. The horizontal shear stresses due to mantle convection and the vertical stress due to the mantle plume are taken as the lower boundary value at the base of the lithosphere, and no stress at the upper boundary value of the lithospheric shell. The stress tensor and maximum stress directions are computed at the Moho boundary in three scenarios: considering horizontal shear stresses due to mantle convection, vertical stresses due to mantle plume, and their combination. The estimated maximum horizontal shear stresses’ locations are consistent with tectonics and seismic activities in the study area. In addition, the maximum shear stress directions are highly correlated with the World Stress Map 2016, especially when the effect of the mantle plume is solely considered, indicating the stress in the study area mainly comes from the plume.

Новые подходы к прогнозированию крупных месторождений стратегических металлов

Synthesis of the obtained materials by sources of metals, agents of their transportation and areas of deposition or accumulation of ores makes it possible to zone the most promising territories to identify new large deposits of strategic metals. As a result of research the main ore-forming systems – sources of strategic metals are identified; a database of deposits and promising ore occurrences of strategic and high-tech metals of Russia has been created; geological and genetic models have been prepared, and on their basis predictive prospecting models of large deposits of strategic metals; new approaches to forecasting large deposits of strategic metals have been developed, including on the basis of data from the GOCE (Gravity Field and Steady-State Ocean Circulation Explorer) spacecraft, which allow using elements of the deep structure of the Earth's crust in predictive prospecting models; a series of predictive metallogenic maps of the territory of various regions of Russia has been compiled.

Assessment of gravity field recovery from a quantum satellite mission with atomic clocks and cold atom gradiometers

The aim of the MOCAST+ (MOnitoring mass variations by Cold Atom Sensors and Time measures) project, which was carried out during the years 2020–2022, was the investigation of the performance of a gravity field mission based on the integration of atomic clocks and cold atom interferometers. The idea was that the combined observations of the two sensors would be beneficial for the detection and monitoring of geophysical phenomena which have an impact on the time-variable part of the Earth gravity field models. Several different mission scenarios were simulated, considering different satellite configurations such as a Gravity Recovery and Climate Experiment (GRACE)-class formation and a Bender-class formation with either two or three in-line satellites along each orbit. Moreover, different atomic species (rubidium and strontium), different inter-satellite distances, different noise power spectral densities, and different observation rates were taken into account. For the gravity field estimation from the simulated data, the space-wise approach was exploited. The results showed that, as it could be expected, the Bender configuration provides significantly better monthly gravity field solutions, as compared to a ‘nominal’ configuration with two or three satellites in a GRACE-class formation. In this way, and pushing the quantum sensors technology to its limits, it is in fact possible to obtain results which are comparable with those from GRACE at low harmonic degrees, and are better at higher degrees with positive effects in the detectability of localized time variable phenomena, as well as in the determination of the static gravity field at a higher maximum spherical harmonic degree than the one achieved by Gravity Field and Steady-State Ocean Circulation Explorer (of course considering an equivalent mission life-time).

Machine learning-based calibration of the GOCE satellite platform magnetometers

Additional datasets from space-based observations of the Earth’s magnetic field are of high value to space physics and geomagnetism. The use of platform magnetometers from non-dedicated satellites has recently successfully provided additional spatial and temporal coverage of the magnetic field. The Gravity and steady-state Ocean Circulation Explorer (GOCE) mission was launched in March 2009 and ended in November 2013 with the purpose of measuring the Earth’s gravity field. It also carried three platform magnetometers onboard. Careful calibration of the platform magnetometers can remove artificial disturbances caused by other satellite payload systems, improving the quality of the measurements. In this work, a machine learning-based approach is presented that uses neural networks to achieve a calibration that can incorporate a variety of collected information about the satellite system. The evaluation has shown that the approach is able to significantly reduce the calibration residual with a mean absolute residual of about 6.47nT for low- and mid-latitudes. In addition, the calibrated platform magnetometer data can be used for reconstructing the lithospheric field, due to the low altitude of the mission, and also observing other magnetic phenomena such as geomagnetic storms. Furthermore, the inclusion of the calibrated platform magnetometer data also allows improvement of geomagnetic field models. The calibrated dataset is published alongside this work.Graphical

Assessment of Global Geopotential Models for Modelling Malaysia Marine Geoid

The evaluation towards global geopotential models represents a significant part in modelling the localised Marine Geoid. The marine geoid provides the vertical reference information in Marine Spatial Data Infrastructures (MSDI) development response to United Nations Sustainable Development Goals 14 for the sustainable development in marine environment. The main purpose of this study is to select the best model from both combined missions and satellite-only missions for the Malaysian region. The gravity anomaly field from 30 global models were exclusively calculated over the selected study area within 11 years period-time. Afterwards, each dataset was extracted from the ICGEM server to evaluate with the airborne-derived gravity anomaly from the Department of Surveying and Mapping, Malaysia. The internal accuracy, root mean square error (RMSE) and differences between every model and airborne data were computed. The result indicates GGM-derived gravity anomaly for the best combined mission is GECO with RMSE of 8.44 mGal and the standard deviation value of 28.034 mGal. While, the model from Gravity field and steady state Ocean Circulation Explorer (GOCE) namely, the GO_CONS_GCF_2_DIR_R5 is the best for the satellite-only mission with RMSE of 17.43 mGal and the standard deviation value of 22.828 mGal. As a conclusion, GECO model is preferred as the best fit for determining the marine geoid as it has the lowest RMSE value between both mission and the maximum degree of 2109ocoverage. The finding can assist in development of marine geoid for modelling precise surface elevation.

High-precision attitude determination using spaceborne gravity gradiometer and gyroscope

This study investigates the application of a spaceborne gravity gradiometer to spacecraft attitude determination. Considering that the gradiometer raw measurements are influenced by angular rotation, a gyroscope is integrated to provide angular velocity information. To deal with unknown biases in both gradiometer and gyroscope measurements, a multiplicative extended Kalman filter (MEKF) is developed to estimate the attitude states and the instrument biases simultaneously. In addition, the cross-correlation between gyroscope measurements and gyroscope-compensated gradiometer measurements is analyzed. The MEKF algorithm is modified accordingly to cope with the correlation problem. Simulation scenarios with two different attitude modes are built to test the algorithm. With a gradiometer of 0.1 E (1 E = 10−9 s−2) accuracy and a navigation-grade gyroscope, attitude determination accuracy of several arcsecs is obtained. Real data from the GOCE (gravity field and steady-state ocean circulation explorer) spacecraft are also used to test the algorithm. Yaw, pitch, and roll angle errors of 2.8 arcsec, 20.9 arcsec, and 11.3 arcsec are achieved, respectively. The method can directly estimate a spacecraft's attitude relative to the Earth-centered Earth-fixed (ECEF) frame and is promising for high-precision spacecraft attitude determination in Earth-oriented missions.

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.