GRACE gravity field recovery with background model uncertainties

Abstract In this article, we present a computationally efficient method to incorporate background model uncertainties into the gravity field recovery process. While the geophysical models typically used during the processing of GRACE data, such as the atmosphere and ocean dealiasing product, have been greatly improved over the last years, they are still a limiting factor of the overall solution quality. Our idea is to use information about the uncertainty of these models to find a more appropriate stochastic model for the GRACE observations within the least squares adjustment, thus potentially improving the gravity field estimates. We used the ESA Earth System Model to derive uncertainty estimates for the atmosphere and ocean dealiasing product in the form of an autoregressive model. To assess our approach, we computed time series of monthly GRACE solutions from L1B data in the time span of 2005 to 2010 with and without the derived error model. Intercomparisons between these time series show that noise is reduced on all spatial scales, with up to 25% RMS reduction for Gaussian filter radii from 250 to 300 km, while preserving the monthly signal. We further observe a better agreement between formal and empirical errors, which supports our conclusion that used uncertainty information does improve the stochastic description of the GRACE observables.

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Multiresolution wavelet analysis applied to GRACE range rate residuals

10.5194/gi-2018-50 ◽

2019 ◽

Cited By ~ 1

Author(s):

Saniya Behzadpour ◽

Torsten Mayer-Gürr ◽

Jakob Flury ◽

Beate Klinger ◽

Sujata Goswami

Keyword(s):

Wavelet Analysis ◽

Gravity Field ◽

Recovery Process ◽

Ocean Tide ◽

Discrete Wavelet ◽

Error Sources ◽

Gravity Field Recovery ◽

Multi Resolution Analysis ◽

Range Rate ◽

Process Observation

Abstract. For further improvements of gravity field models based on Gravity Recovery and Climate Experiment (GRACE) observations, it is necessary to identify the error sources within the recovery process. Observation residuals obtained during the gravity field recovery contain most of the measurement and modeling errors and thus can be considered as a realization of actual errors. In this work, we investigate the ability of wavelets to help in identifying specific error sources in GRACE range rate residuals. The Multi-Resolution Analysis (MRA) using Discrete Wavelet Transform (DWT) is applied to decompose the residual signal into different scales with corresponding frequency bands. Temporal, spatial, and orbit-related features of each scale are then extracted for further investigations. The wavelet analysis has proved to be a practical tool to find the main error contributors. Beside the previously known sources such as K-Band Ranging (KBR) system noise and systematic attitude variations, this method clearly shows effects which the classic spectral analysis is hardly able or unable to represent. These effects include long-term signatures due to satellite eclipse crossings and dominant ocean tide errors.

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GOCE SGG and SST quick-look gravity field analysis

Advances in Geosciences ◽

10.5194/adgeo-1-5-2003 ◽

2003 ◽

Vol 1 ◽

pp. 5-9 ◽

Cited By ~ 9

Author(s):

R. Pail ◽

M. Wermut

Keyword(s):

Time Series ◽

Gravity Field ◽

Point Of View ◽

Field Analysis ◽

Measurement Time ◽

Practical Case ◽

Theoretical Point ◽

Satellite Gravity ◽

Gravity Field Recovery ◽

Data Gaps

Abstract. The purpose of quick-look analysis in the framework of the GOCE data processing architecture is to analyse partial data sets of satellite gravity gradiometry (SGG) and satellite-to-satellite tracking in high-low mode (hl-SST), in order to derive a diagnosis of the system performance. The semi-analytic (SA) method for gravity field recovery from GOCE observations, which is based on Fast Fourier Transform, is used. From a theoretical point of view, a number of requirements (circular, exact repeat orbit, uninterrupted measurement time series) have to be fulfilled. However, in the present paper it is demonstrated, that the SA approach can also be applied in the practical case of non-circular, nonrepeat orbits, and data gaps in the GOCE measurement time series. The performance of this approach is assessed in 5 case studies on the basis of a realistic closed-loop simulation.Key words. GOCE – semi-analytic approach – colored noise – data gaps – repeat orbit

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Time-variable gravity field recovery from kinematic positions of Low Earth Orbiting satellites

10.5194/egusphere-egu21-7708 ◽

2021 ◽

Author(s):

Thomas Grombein ◽

Martin Lasser ◽

Daniel Arnold ◽

Ulrich Meyer ◽

Adrian Jäggi

Keyword(s):

Time Series ◽

Gravity Field ◽

Time Variable ◽

Kinematic Orbit ◽

Time Variable Gravity ◽

Gravity Field Recovery ◽

The Earth ◽

Leo Satellites ◽

Variable Gravity ◽

Gnss Data

For the monitoring of mass transport and mass distribution in the Earth&#8217;s system, the gravity field and its temporal variations provide an important source of information. Dedicated satellite missions like GRACE and GRACE-FO allow to resolve the Earth&#8217;s time-variable gravity field based on ultra-precise inter-satellite ranging. In addition, any (non-dedicated) Low Earth Orbiting (LEO) satellite equipped with an on-board GNSS receiver may also serve as a gravity field sensor. For this purpose, the collected GNSS data is used to derive kinematic LEO orbit positions that can subsequently be utilized as pseudo-observations for gravity field recovery. Although this technique is less sensitive and restricted to the long wavelength part of the gravity field, it provides valuable information, particularly for those months where no inter-satellite ranging measurements are available from GRACE or GRACE-FO. Furthermore, the increasing number of operational LEO satellites makes it attractive to produce combined Multi-LEO gravity field solutions that will take advantage of the variety of complementary orbital configurations and can offer additional sensitivities to selected coefficients of solutions based on inter-satellite ranging.At the Astronomical Institute of the University of Bern (AIUB) GPS-based kinematic orbits are routinely processed for various LEO satellites like missions dedicated to gravity (GOCE, GRACE/-FO), altimetry (Jason, Sentinel), or further constellations of Earth-observing satellites like SWARM. Beside conventional ambiguity-float orbits, also ambiguity-fixed orbits are recently being computed based on new phase bias and clock products of the Center for Orbit Determination in Europe (CODE). The kinematic orbit positions offer the opportunity to derive time series of monthly gravity field solutions for the different LEO satellites that are eventually combined on the level of normal equations.In this contribution, we will present first results of our effort to generate a combined time series of monthly gravity field solutions based on the kinematic orbits of multiple LEO satellites. In a first step, the focus is laid on the GRACE/-FO missions that provide the longest time series in terms of collected GNSS data and that will therefore serve as a backbone for future combinations. We analyze the impact of accelerometer data on the recovery of time-variable mass variations. This will be particularly important for the handling of non-dedicated gravity missions, for which accelerometer measurements are usually not available. Furthermore, we study and compare the performance of gravity field recoveries based on ambiguity-float and ambiguity-fixed kinematic orbit solutions. We assess our results with respect to superior gravity field models based on inter-satellite ranging for selected areas with strong mass change signals like in Greenland, West-Antarctica or the Amazon river basin.

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Multiresolution wavelet analysis applied to GRACE range-rate residuals

Geoscientific Instrumentation Methods and Data Systems ◽

10.5194/gi-8-197-2019 ◽

2019 ◽

Vol 8 (2) ◽

pp. 197-207 ◽

Cited By ~ 1

Author(s):

Saniya Behzadpour ◽

Torsten Mayer-Gürr ◽

Jakob Flury ◽

Beate Klinger ◽

Sujata Goswami

Keyword(s):

Wavelet Analysis ◽

Gravity Field ◽

Recovery Process ◽

Ocean Tide ◽

Discrete Wavelet ◽

Error Sources ◽

Gravity Field Recovery ◽

Range Rate ◽

Process Observation ◽

Gravity Recovery

Abstract. For further improvements of gravity field models based on Gravity Recovery and Climate Experiment (GRACE) observations, it is necessary to identify the error sources within the recovery process. Observation residuals obtained during the gravity field recovery contain most of the measurement and modeling errors and thus can be considered a realization of actual errors. In this work, we investigate the ability of wavelets to help in identifying specific error sources in GRACE range-rate residuals. The multiresolution analysis (MRA) using discrete wavelet transform (DWT) is applied to decompose the residual signal into different scales with corresponding frequency bands. Temporal, spatial, and orbit-related features of each scale are then extracted for further investigations. The wavelet analysis has proven to be a practical tool to find the main error contributors. Besides the previously known sources such as K-band ranging (KBR) system noise and systematic attitude variations, this method clearly shows effects which the classic spectral analysis is hardly able or unable to represent. These effects include long-term signatures due to satellite eclipse crossings and dominant ocean tide errors.

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Future Satellite Gravity Missions enhanced by Cold Atom Interferometry Accelerometers

10.5194/egusphere-egu21-7612 ◽

2021 ◽

Author(s):

Annike Knabe ◽

Hu Wu ◽

Manuel Schilling ◽

Alireza HosseiniArani ◽

Jürgen Müller ◽

...

Keyword(s):

Gravity Field ◽

Inertial Sensors ◽

Cold Atom ◽

Atom Interferometry ◽

Limiting Factor ◽

Lower Saxony ◽

Satellite Gravity ◽

German Research Foundation ◽

Gravity Field Recovery ◽

Satellite Gravity Missions

Satellite gravity missions, like GRACE and GRACE Follow-On, successfully map the Earth&#8217;s gravity field and its changes, but the boundaries of spatial and temporal resolution need to be pushed further. The major enhancement from GRACE to GRACE-FO is the laser interferometry instrument which enables a much more accurate inter-satellite ranging. However, the accelerometers used for observing the non-conservative forces have merely been improved and are one major limiting factor for gravity field recovery. Inertial sensors based on cold atom interferometry (CAI) show promising characteristics, especially their long-term stability at frequencies below 10^-3 Hz is very beneficial. The CAI concept has already been successfully demonstrated in ground experiments. In space, an even higher sensitivity is expected due to increased interrogation time of one interferometer measurement cycle.In this contribution, we investigate potential next-generation gravity missions (NGGM) following the GRACE design, employing an LRI with GRACE-FO characteristics and the utilisation of CAI accelerometry. The combination of CAI technology with a classic electrostatic accelerometer is evaluated as well. The sensor performances are tested via closed-loop simulations for different scenarios and the recovered gravity field results are evaluated. In order to achieve a realistic model of the atomic interferometer, noise levels depending on the architecture of the sensor and its transfer function are included. Here, also the effect of variations of the non-gravitational accelerations during one interferometer cycle is analyzed.Another crucial aspect for satellite missions is the drag compensation. Its requirement is reduced by two orders of magnitude when using a CAI accelerometer due to its better known scale factor. The feasibility of such requirements is assessed with respect to simulated satellite dynamics for several altitudes and drag compensation parameters.H.W. acknowledges support by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy &#8211; EXC 2123 &#8220;QuantumFrontiers, Project-ID 390837967&#8220;. A.K. acknowledges initial funding for the DLR Institute by the Ministry of Science and Culture of the German State of Lower Saxony from &#8220;Nieders&#228;chsisches Vorab&#8221;. A.H. acknowledges support by DLR-Institute for Satellite Geodesy and Inertial Sensing.

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Adjoint-based direct data assimilation of GNSS time series for optimizing frictional parameters and predicting postseismic deformation following the 2003 Tokachi-oki earthquake

Earth Planets and Space ◽

10.1186/s40623-020-01293-0 ◽

2020 ◽

Vol 72 (1) ◽

Author(s):

Masayuki Kano ◽

Shin’ichi Miyazaki ◽

Yoichi Ishikawa ◽

Kazuro Hirahara

Keyword(s):

Time Series ◽

Data Assimilation ◽

Evaluation Method ◽

Temporal Evolution ◽

Recovery Process ◽

Postseismic Deformation ◽

Coseismic Slip ◽

Megathrust Earthquakes ◽

Spatio Temporal ◽

Gnss Time Series

Abstract Postseismic Global Navigation Satellite System (GNSS) time series followed by megathrust earthquakes can be interpreted as a result of afterslip on the plate interface, especially in its early phase. Afterslip is a stress release process accumulated by adjacent coseismic slip and can be considered a recovery process for future events during earthquake cycles. Spatio-temporal evolution of afterslip often triggers subsequent earthquakes through stress perturbation. Therefore, it is important to quantitatively capture the spatio-temporal evolution of afterslip and related postseismic crustal deformation and to predict their future evolution with a physics-based simulation. We developed an adjoint data assimilation method, which directly assimilates GNSS time series into a physics-based model to optimize the frictional parameters that control the slip behavior on the fault. The developed method was validated with synthetic data. Through the optimization of frictional parameters, the spatial distributions of afterslip could roughly (but not in detail) be reproduced if the observation noise was included. The optimization of frictional parameters reproduced not only the postseismic displacements used for the assimilation, but also improved the prediction skill of the following time series. Then, we applied the developed method to the observed GNSS time series for the first 15 days following the 2003 Tokachi-oki earthquake. The frictional parameters in the afterslip regions were optimized to A–B ~ O(10 kPa), A ~ O(100 kPa), and L ~ O(10 mm). A large afterslip is inferred on the shallower side of the coseismic slip area. The optimized frictional parameters quantitatively predicted the postseismic GNSS time series for the following 15 days. These characteristics can also be detected if the simulation variables can be simultaneously optimized. The developed data assimilation method, which can be directly applied to GNSS time series following megathrust earthquakes, is an effective quantitative evaluation method for assessing risks of subsequent earthquakes and for monitoring the recovery process of megathrust earthquakes.

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Earth’s Time-Variable Gravity from GRACE Follow-On K-Band Range-Rates and Pseudo-Observed Orbits

Remote Sensing ◽

10.3390/rs13091766 ◽

2021 ◽

Vol 13 (9) ◽

pp. 1766

Author(s):

Igor Koch ◽

Mathias Duwe ◽

Jakob Flury ◽

Akbar Shabanloui

Keyword(s):

Gravity Field ◽

Time Variable ◽

Time Variable Gravity ◽

Gravity Field Recovery ◽

Variable Gravity ◽

Earth’S System ◽

Grace Mission ◽

Insight Into ◽

K Band

During its science phase from 2002–2017, the low-low satellite-to-satellite tracking mission Gravity Field Recovery And Climate Experiment (GRACE) provided an insight into Earth’s time-variable gravity (TVG). The unprecedented quality of gravity field solutions from GRACE sensor data improved the understanding of mass changes in Earth’s system considerably. Monthly gravity field solutions as the main products of the GRACE mission, published by several analysis centers (ACs) from Europe, USA and China, became indispensable products for quantifying terrestrial water storage, ice sheet mass balance and sea level change. The successor mission GRACE Follow-On (GRACE-FO) was launched in May 2018 and proceeds observing Earth’s TVG. The Institute of Geodesy (IfE) at Leibniz University Hannover (LUH) is one of the most recent ACs. The purpose of this article is to give a detailed insight into the gravity field recovery processing strategy applied at LUH; to compare the obtained gravity field results to the gravity field solutions of other established ACs; and to compare the GRACE-FO performance to that of the preceding GRACE mission in terms of post-fit residuals. We use the in-house-developed MATLAB-based GRACE-SIGMA software to compute unconstrained solutions based on the generalized orbit determination of 3 h arcs. K-band range-rates (KBRR) and kinematic orbits are used as (pseudo)-observations. A comparison of the obtained solutions to the results of the GRACE-FO Science Data System (SDS) and Combination Service for Time-variable Gravity Fields (COST-G) ACs, reveals a competitive quality of our solutions. While the spectral and spatial noise levels slightly differ, the signal content of the solutions is similar among all ACs. The carried out comparison of GRACE and GRACE-FO KBRR post-fit residuals highlights an improvement of the GRACE-FO K-band ranging system performance. The overall amplitude of GRACE-FO post-fit residuals is about three times smaller, compared to GRACE. GRACE-FO post-fit residuals show less systematics, compared to GRACE. Nevertheless, the power spectral density of GRACE-FO and GRACE post-fit residuals is dominated by similar spikes located at multiples of the orbital and daily frequencies. To our knowledge, the detailed origin of these spikes and their influence on the gravity field recovery quality were not addressed in any study so far and therefore deserve further attention in the future. Presented results are based on 29 monthly gravity field solutions from June 2018 until December 2020. The regularly updated LUH-GRACE-FO-2020 time series of monthly gravity field solutions can be found on the website of the International Centre for Global Earth Models (ICGEM) and in LUH’s research data repository. These operationally published products complement the time series of the already established ACs and allow for a continuous and independent assessment of mass changes in Earth’s system.

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GRACETOOLS—GRACE Gravity Field Recovery Tools

Geosciences ◽

10.3390/geosciences8090350 ◽

2018 ◽

Vol 8 (9) ◽

pp. 350 ◽

Cited By ~ 1

Author(s):

Neda Darbeheshti ◽

Florian Wöske ◽

Matthias Weigelt ◽

Christopher Mccullough ◽

Hu Wu

Keyword(s):

Open Source ◽

Gravity Field ◽

Transition Matrix ◽

State Transition ◽

Satellite Observations ◽

Gravity Field Recovery ◽

Grace Data ◽

Range Rate ◽

Analysis Platform ◽

Recovery Tools

This paper introduces GRACETOOLS, the first open source gravity field recovery tool using GRACE type satellite observations. Our aim is to initiate an open source GRACE data analysis platform, where the existing algorithms and codes for working with GRACE data are shared and improved. We describe the first release of GRACETOOLS that includes solving variational equations for gravity field recovery using GRACE range rate observations. All mathematical models are presented in a matrix format, with emphasis on state transition matrix, followed by details of the batch least squares algorithm. At the end, we demonstrate how GRACETOOLS works with simulated GRACE type observations. The first release of GRACETOOLS consist of all MATLAB M-files and is publicly available at Supplementary Materials.

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Scale-dependent intrinsic entropies of complex time series

Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rsta.2015.0204 ◽

2016 ◽

Vol 374 (2065) ◽

pp. 20150204 ◽

Cited By ~ 2

Author(s):

Jia-Rong Yeh ◽

Chung-Kang Peng ◽

Norden E. Huang

Keyword(s):

Time Series ◽

Time Scales ◽

Spatial Scales ◽

Multiple Time Scales ◽

Multiple Time ◽

Complex Time ◽

Multi Scale ◽

Mode Decomposition ◽

Simulated Time ◽

Simulated Time Series

Multi-scale entropy (MSE) was developed as a measure of complexity for complex time series, and it has been applied widely in recent years. The MSE algorithm is based on the assumption that biological systems possess the ability to adapt and function in an ever-changing environment, and these systems need to operate across multiple temporal and spatial scales, such that their complexity is also multi-scale and hierarchical. Here, we present a systematic approach to apply the empirical mode decomposition algorithm, which can detrend time series on various time scales, prior to analysing a signal’s complexity by measuring the irregularity of its dynamics on multiple time scales. Simulated time series of fractal Gaussian noise and human heartbeat time series were used to study the performance of this new approach. We show that our method can successfully quantify the fractal properties of the simulated time series and can accurately distinguish modulations in human heartbeat time series in health and disease.

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GRACE Follow-On Gravity Field Recovery from Combined Laser Ranging Interferometer and Microwave Ranging System Measurements

10.5194/egusphere-egu21-9415 ◽

2021 ◽

Author(s):

Saniya Behzadpour ◽

Andreas Kvas ◽

Torsten Mayer-Gürr

Keyword(s):

Gravity Field ◽

Laser Ranging ◽

Measurement Technology ◽

Additional Measurement ◽

Covariance Functions ◽

Gravity Field Recovery ◽

Global Gravity ◽

Least Squares Adjustment ◽

Noise Covariance ◽

Component Estimation

Besides a K-Band Ranging System (KBR), GRACE-FO carries a Laser Ranging Interferometer (LRI) as a technology demonstration to provide measurements of inter-satellite range changes. This additional measurement technology provides supplementary observations, which allow for cross-instrument diagnostics with the KBR system and, to some extent, the separation of ranging noise from other sources such as noise in the on-board accelerometer (ACC) measurements.The aim of this study is to incorporate the two ranging systems (LRI and KBR) observations in ITSG-Grace2018 gravity field recovery. The two observation groups are combined in an iterative least-squares adjustment with variance component estimation used to determine the unknown noise covariance functions for KBR, LRI, and ACC measurements. We further compare the gravity field solutions obtained from the combined solutions to KBR-only results and discuss the differences with a focus on the global gravity field and LRI calibration parameters.

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