ALBERT

Description: With knowledge of geometry and density-distribution of topography, the residual terrain modelling (RTM) technique has been broadly applied in geodesy and geophysics for the determination of the high-frequency gravity field signals. Depending on the size of investigation areas, challenges in computational efficiency are encountered when using an ultra-high-resolution digital elevation model (DEM) in the Newtonian integration. For efficient and accurate gravity forward modelling in the spatial domain, we developed a new MATLAB-based program called, terrain gravity field (TGF). Our new software is capable of calculating the gravity field generated by an arbitrary topographic mass-density distribution. Depending on the attenuation character of gravity field with distance, the adaptive algorithm divides the integration masses into four zones, and adaptively combines four types of geometries (i.e., polyhedron, prism, tesseroid and point-mass) and DEMs with different spatial resolutions. Compared to some publicly available algorithms depending on one type of geometric approximation, this enables accurate modelling of gravity field and greatly reduces the computation time. Besides, the TGF software allows to calculate ten independent gravity field functionals, supports two types of density inputs (constant density value and digital density map), and considers the curvature of the Earth by involving spherical approximation and ellipsoidal approximation. Further to this, the TGF software is also capable of delivering the gravity field of full-scale topographic gravity field implied by masses between the Earth’s surface and mean sea level. In this contribution, the TGF software is introduced to the geoscience community and its capabilities are explained. Results from internal and external numerical validation experiments of TGF confirmed its accuracy at the sub-mGal level. Based on TGF, the trade-off between accuracy and efficiency, values for the spatial resolution and extension of topography models are recommended. The TGF software has been extensively tested and recently been applied in the SRTM2gravity project to convert the global 3” SRTM topography to implied gravity effects at 28 billion computation points. This confirms the capability of TGF for dealing with large datasets. Together with this paper, the TGF software will be released in the public domain for free use in geodetic and geophysical forward modelling computations.

Description: Various types of heterogeneous observations can be combined within a parameter estimation process using spherical radial basis functions (SRBFs) for regional gravity field refinement. In this process, regularization is in most cases inevitable, and choosing an appropriate value for the regularization parameter is a crucial issue. This study discusses the drawbacks of two frequently used methods for choosing the regularization parameter, which are the L-curve method and the variance component estimation (VCE). To overcome their drawbacks, two approaches for the regularization parameter determination are proposed, which combine the L-curve method and VCE. The first approach, denoted as “VCE-Lc”, starts with the calculation of the relative weights between the observation techniques by means of VCE. Based on these weights, the L-curve method is applied to determine the regularization parameter. In the second approach, called “Lc-VCE”, the L-curve method determines first the regularization parameter, and it is set to be fixed during the calculation of the relative weights between the observation techniques from VCE. To evaluate and compare the performance of the two proposed methods with the L-curve method and VCE, all these four methods are applied in six study cases using four types of simulated observations in Europe, and their modeling results are compared with the validation data. The RMS errors (w.r.t the validation data) obtained by VCE-Lc and Lc-VCE are smaller than those obtained from the L-curve method and VCE in all the six cases. VCE-Lc performs the best among these four tested methods, no matter if using SRBFs with smoothing or non-smoothing features. These results prove the benefits of the two proposed methods for regularization parameter determination when different data sets are to be combined.

Description: 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

Description: Temporal gravity retrieval simulation results of a future Bender-type double pair mission concept, performed by five processing centers of a Sino-European study team, have been inter-compared and assessed. They were computed in a synthetic closed-loop simulation world by five independent software systems applying different gravity retrieval methods, but were based on jointly defined mission scenarios. The inter-comparison showed that the results achieved a quite similar performance. Exemplarily, the root mean square (RMS) deviations of global equivalent water height fields from their true reference, resolved up to degree and order 30 of a 9-day solution, vary in the order of 10% of the target signal. Also, co-estimated independent daily gravity fields up to degree and order 15, which have been co-estimated by all processing centers, do not show large differences among each other. This positive result is an important pre-requisite and basis for future joint activities towards the realization of next-generation gravity missions.

Description: In this study the feasibility and performance of time variable decorrelation (VADER) filters derived from covariance information on decadal Gravity Recovery and Climate Experiment (GRACE) time series are investigated. The VADER filter is based on publicly available data that are provided by several GRACE processing centers, and does not need its own Level-2 processing chain. Numerical closed loop simulations, incorporating stochastic and deterministic error budgets, serve as basis for the design of the filter setup, and the resulting filters are subsequently applied for real data processing. The closed loop experiments demonstrate the impact of temporally varying error and signal covariance matrices that are used for the design of decorrelation filters. The results indicate an average reduction of cumulative geoid height errors of 15% using time-variable instead of static decorrelation. Based on the simulation experience, a real data filtering procedure is designed and set up. It is applied to the ITSG-Grace2014 time variable gravity field time series with its associated full monthly covariance matrices. To assess the validity of the approach, linear mass trend estimates for the Antarctic Peninsula are computed using VADER filters and compared to previous estimates from both, GRACE and other mass balance estimation techniques. The mass change results obtained show very good agreement with other estimates and are robust against variations of the filter strength. The DDK decorrelation filter serves as main benchmark for the assessment of the VADER filter. For comparable filter strengths the VADER filters achieve a better de-striping and deliver smaller formal errors than static filters like the DDK.

Description: Past temporal gravity field solutions from the Gravity Recovery and Climate Experiment (GRACE), as well as current solutions from GRACE Follow-On, suffer from temporal aliasing errors due to undersampling of the signal to be recovered (e.g., hydrology), which arise in terms of stripes caused by the north–south observation direction. In this paper, we investigate the potential of the proposed mass variation observing system by high–low inter-satellite links (MOBILE) mission. We quantify the impact of instrument errors of the main sensors (inter-satellite link and accelerometer) and high-frequency tidal and non-tidal gravity signals on achievable performance of the temporal gravity field retrieval. The multi-directional observation geometry of the MOBILE concept with a strong dominance of the radial component result in a close-to-isotropic error behavior, and the retrieved gravity field solutions show reduced temporal aliasing errors of at least 30% for non-tidal, as well as tidal, mass variation signals compared to a low–low satellite pair configuration. The quality of the MOBILE range observations enables the application of extended alternative processing methods leading to further reduction of temporal aliasing errors. The results demonstrate that such a mission can help to get an improved understanding of different components of the Earth system.

Description: The goal of next-generation gravity missions (NGGM) is to improve the monitoring of mass transport in the Earth system by an increased space-time sampling capability as well as higher accuracies of a new generation of instrumentation, but also to continue the monitoring time series obtained by past and current missions such as GRACE and GRACE Follow-On. As the likelihood of three satellite pairs being simultaneously in orbit in the mid-term future increased, we have performed a closed-loop simulation to investigate the impact of a third pair in either polar or inclined orbit as an addition to a Bender-type constellation with NGGM instrumentation. For the additional pair, GRACE-like as well as NGGM instrumentation was tested. The analysis showed that the third pair mainly increases the redundancy of the monitoring system but does not significantly improve de-aliasing capabilities. The best-performing triple-pair scenario comprises a third inclined pair with NGGM sensors. Starting with a Bender-type constellation of a polar and an inclined satellite pair, simulation results indicate an average improvement of 11% in case of adding the third pair in a near-polar orbit, and of 21% for the third pair placed in an inclined orbit. The most important advantage of a multi-pair constellation, however, is the possibility to recover daily gravity fields with higher spatial resolution. In the case of the investigated triple-pair scenarios, a meaningful daily resolution with a maximum spherical harmonic degree of 26 can be achieved, while a higher daily parametrization up to degree 40 results in spatial aliasing and thus would need additional constraints or prior information.

Description: Climate change will affect the terrestrial water cycle during the next decades by impacting the seasonal cycle, interannual variations, and long-term linear trends of water stored at or beyond the surface. Since 2002, terrestrial water storage (TWS) has been globally observed by the Gravity Recovery and Climate Experiment (GRACE) and its follow-on mission (GRACE-FO). Next Generation Gravity Missions (NGGMs) are planned to extend this record in the near future. Based on a multi-model ensemble of climate model output provided by the Coupled Model Intercomparison Project Phase 6 (CMIP6) covering the years 2002–2100, we assess possible changes in TWS variability with respect to present-day conditions to help defining scientific requirements for NGGMs. We find that present-day GRACE accuracies are sufficient to detect amplitude and phase changes in the seasonal cycle in a third of the land surface, whereas a five times more accurate double-pair mission could resolve such changes almost everywhere outside the most arid landscapes of our planet. We also select one individual model experiment out of the CMIP6 ensemble that closely matches both GRACE observations and the multi-model median of all CMIP6 realizations, which might serve as basis for satellite mission performance studies extending over many decades to demonstrate the suitability of NGGM satellite missions to monitor long-term climate variations in the terrestrial water cycle.