Session: A.1 - Analysis Techniques
(Convener: )

Title: The V03 Level-1 Release
Presenter: Sakumura, Carly
Co-Authors: N. Harvey, T. Bandikova, C. McCullough

Abstract: The V03 reprocessing campaign for GRACE Level-1 data was initiated to correct errors in the current GRACE products identified in Bandikova (2014), Harvey (2016) and improve the spacecraft attitude reconstruction. The current attitude determination process is complicated by regular blinding of one or both cameras from the sun and moon, correlated error in the star camera field of view, and determination of instrument alignment. The V03 SCA1B products are generated via a Kalman filter algorithm to combine the star camera and accelerometer data into a higher fidelity attitude solution with more accurate instrument noise models. The V03 products show fewer gaps, eliminate jumps in the solution when switching between dual and single camera data, and reduce high frequency noise. In this study we present the status of the reprocessing campaign, an overview of the noise models and strategy, and the impact of the V03 reprocessing campaign on Level-2 gravity field products.

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Title: New RL04 CNES/GRGS gravity field solutions
Presenter: Biancale, Richard
Co-Authors: J. Lemoine, S. Bourgogne

Abstract: After more than 15 years of GRACE mission, the data processing for gravity field recovery has slightly evolved. That is true in particular for the STAR and KBR calibration parameters and even for modelling the gravity field itself.

The new version of monthly/10-day GRGS models: GRGS RL04 wants to correct some small deficiencies appeared previously as in other realizations.

We propose to present the new standards for RL04 models in terms of processing standards, inversion technique, as well as validation tests across geographical areas.

The new models expand up to degree/order 90 in terms of spherical harmonics. They are processed in successive steps. They can be downloaded at: grgs.obs-mip.fr/grace, and directly visualized in terms of time-series at: thegraceplotter.com.

In addition, we present alternative hybrid solutions which combine spherical harmonic expansions up to degree 25 and 2deg.*2deg. surface masses over the continents. Introducing discretized surface masses helps for instance to avoid some damping along coasts presenting strong gravity variations.

Both solution types are then compared over a few areas as quality indicators.

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Title: NASA GSFC mascons: Advancements in signal covariance design and the estimation of noise uncertainties and leakage errors
Presenter: Loomis, Bryant
Co-Authors: S. B. Luthcke, T. Sabaka, K. Rachlin

Abstract: The key design parameter in producing time-variable gravity mascons is the set of signal covariance matrices applied in the regularized least squares estimation. We present the improved iterative solution approach from NASA GSFC, which now applies inter-satellite range-acceleration residuals in the construction of the monthly mascon signal covariance matrices, and we demonstrate the quality of this new mascon product. We also present new estimates of the mascon noise uncertainties and signal leakage errors. It is difficult to accurately assess signal leakage, and as a result this significant error source is often ignored. We have computed rigorous estimates of the leakage errors by constructing the full monthly resolution operators and applying them to our monthly solutions. Our new mascon product provides end users with a straightforward approach to assign leakage errors to any subset of mascons, and we discuss recommendations for properly combining the noise uncertainties with the leakage errors to form total estimates of the error.

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Title: Reassessment of the DDK-filter method with actual error covariance information
Presenter: Fagiolini. Elisa
Co-Authors: C. Dahle, M. Murböck

Abstract: The DDK-filter (Kusche 2007) is a decorrelation non-isotropic filter based on a regularization of the normal equation system applying the error and signal covariance matrix. As the error covariance matrix is computed from GRACE observations, it also reflects the actual orbit geometry in a particular month. However, we have to distinguish between the DDK-filter method itself, as described above, and the commonly applied realization of this method, denoted as "Kusche-filter" hereafter. For the latter, ready-to-use filter matrices DDK[1-5] are provided which are based on the error covariance of one single month (August 2003), i.e. the filter is static instead of varying in time.

Since GRACE orbit geometry is varying in time and does not allow to always produce gravity data of the same quality, one could either decide to use a stronger version of the filter (bigger regularization parameter, bigger radius) for those bad months with sparse coverage, or to use a DDK-filter that fits better to the actual quality of the data. We tested these two options comparing the DDK[1-5] "Kusche-filter" with a DDK-filter obtained from realistic error covariance matrices, where “realistic” means:

1. GRACE solutions are filtered with their corresponding individual error covariance matrices, in order to avoid inconsistency between data type;
2. the error covariance matrices are varying in time, in order to include information about changing orbit configuration (such as repeat orbits and lower altitude).

The test is performed with real GFZ RL05a data as well as with simulated data, where the known “truth” can be compared with the different filtered observations.

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Title: Recovering sub-monthly terrestrial water storage variations with a new daily GRACE mascon estimate
Presenter: Croteau, Michael
Co-Authors: B.D. Loomis, R.S. Nerem

Abstract: The GRACE mission has enabled studies of short and long term regional terrestrial water storage (TWS) changes. These studies have primarily been limited to long wavelength signals due to the inherent 30-day temporal resolution associated with most GRACE products. In this study, we seek to improve on this limitation by developing a daily TWS estimate as an additional iteration of the GSFC global mascon solution. In doing so, we supplement the monthly high spatial resolution of the GSFC mascon product with a lower spatial resolution daily least squares estimate. We describe the design of this technique and present initial results from a simulation designed to help quantify the technique's spatial and temporal recoverability and drive the design of our final mascon regularization scheme. From this, we preview daily solution results and discuss ongoing work to further refine the solution and quantify both errors and spatial limitations of the solution.

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Title: Evaluation of AOD1B RL06 over Greenland and Antarctica
Presenter: Hardy, Ryan
Co-Authors: R. S. Nerem; D.N. Wiese

Abstract: Errors in dealiasing models related to model drifts and changes can introduce biases GRACE estimates of mass change within basins. Over Antarctica, errors in AOD1B RL05 spuriously mask acceleration in mass loss on the order of 4 Gt yr-2. Over Greenland, atmospheric errors are a major noise source and introduce a spurious trend of 2 Gt yr-1. The newly released AOD1B RL06 mitigates some of these errors using a higher spatial resolution, more accurate input models, and better control of model-change biases. We preview the effects of AOD1B RL06 on future GRACE releases. Our analysis assesses the accuracy of monthly averages of AOD1B RL06 over Antarctica and Greenland relative to both in situ surface pressure observations and reanalyses. We determine the magnitude of effects, such as spurious accelerations, introduced by the new model. Furthermore, we highlight how differences in product definitions between of AOD1B releases affect this comparison.

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Title: Why Do We Use Range Rate And Not Range Acceleration Observations?
Presenter: Tregoning, Paul
Co-Authors: A. Purcell, S. Allgeyer, H. McQueen, S. McClusky, E-K Potter, T.A. Herring, J-P Montillet

Abstract: Nearly all temporal gravity fields estimated using data from the GRACE mission use the range rate as the key observable. However, the range acceleration observable offers particular advantages over the range rate such as a reduction of correlations in the least squares inversion and better spatial localisation of mass variation signals. Numerical differentiation of the Level-1B inter-satellite range observations yields range rate and range acceleration “observations" which contain substantially less noise than their Level-1B counterparts. The use of these improved observations permits geophys-ical signals on Earth to be seen in the data even before inverting for the temporal gravity field. We find that noise contained in estimates of the temporal gravity field using observations of the GRACE mission can be reduced significantly through the use of these improved inter-satellite range acceleration observations. The geophysical signals on Earth can be seen in the prefit range acceleration residuals even before inverting for the temporal gravity field. We find that the use of the range acceleration leads to much less north/south error striping in the estimated temporal gravity fields. We demonstrate the capability of estimating sub-monthly gravity fields from GRACE data with this approach and show the improvement in the accuracy of the gravity field estimate using time differentiated range accelerations instead of Level-1B range rate. Our approach will also be applicable to data from the GRACE Follow-On mission due for launch in 2018.

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Title: The unexpected signal in GRACE estimates of C20
Presenter: Cheng, Minkang
Co-Authors: J. Ries

Abstract: For science applications of the Gravity Recovery and Climate Experiment (GRACE) monthly solutions, the GRACE estimates of C20 (or J2) are typically replaced by the value determined from Satellite Laser Ranging (SLR) due to an unexpectedly strong variation at a period of ~160 days. Errors in the S2 tide model used in GRACE data processing could produce a significant perturbation to the GRACE orbits, but it cannot contribute to the ~160-day signal appearing in C20. A time series of 138 monthly solutions up to degree and order 10 (10x10) were derived along with estimates of ocean tide parameters up to degree 6 for eight major tides. The results show that the ~160-day signal remains in GRACE estimates of C20. Consequently, the anomalous signal in GRACE C20 cannot be attributed to aliasing from the errors in the S2 tide. A preliminary analysis of the cross-track forces acting on GRACE and the cross-track component of the accelerometer data suggests that a non-geophysical, temperature-dependent systematic error in the accelerometer data could be a cause.

Because a wide variety of science applications rely on the replacement values for C20, it is essential that the SLR estimates are as reliable as possible. Study indicates that the direct combination of GRACE and SLR data might benefit the resonant orders in the GRACE-derived gravity fields, but it appears to degrade the recovery of the C20 variations. The apparently poorer recovery of C40 by GRACE, where the annual variation is significantly underestimated compared to SLR, may be affecting the estimates of C20. Consequently, it appears appropriate to continue using the SLR-based estimates of C20, and possibly also C40, to augment the existing GRACE mission.

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Title: Update to the conventional model for rotational deformation
Presenter: Ries, John
Co-Authors:

Abstract: Rotational deformation (also called the “pole tide”) is the deformation resulting from the centrifugal effect of polar motion on the solid earth and ocean, which manifests itself as variations in ocean heights, in the gravity field and in surface displacements. The model for rotational deformation assumes a primarily elastic response of the Earth to the centrifugal potential at the annual and Chandler periods and applies body tide Love numbers to the polar motion after removing the mean pole. However, the elastic Love numbers should be applicable to longer period variations as well, and only the secular (i.e. linear) mean pole should be removed. The consequences of an updated model for rotational deformation for site motion and the gravity field are illustrated.

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Poster Title: Analyzing the KBR system noise in the range-rate residuals
Presenter: Goswami, Sujata
Co-Authors: B. Devaraju, M. Weigelt, T. Mayer-Gürr, J. Flury, S. Behzadpour

Abstract: An understanding of the noise present in the range-rate observations is important to know the factors responsible for limiting the precision of the gravity field obtained from these observations. The goal is to minimize the existing gap between the current precision level and the predicted baseline. Here, we will analyze errors in the post-fit range-rate residuals contributed by the KBR system noise and discuss their characteristics. We will present the source of the errors affecting the signal-to-noise ratio of the phase observations which are combined to form range-rates. These degraded phase observations when combined to form range-rates increase the noise in the range-rate observations. We will further present the propagation of the errors contributed by the KBR system into the gravity field parameters. We discuss the impact of non-stationary noise characteristics on the gravity field coefficients which are helpful in improving the existing data processing strategies used to compute gravity field solutions.

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Poster Title: Simultaneous Processing of Global GPS and GRACE Observations: Toward a Unified Solution for the Geopotential and Terrestrial Reference Frame
Presenter: Haines, Bruce
Co-Authors: W. Bertiger, S. Desai. N. Harvey, D. Kuang, M. Miller, A. Sibois and D. Yuan

Abstract: We describe a unified approach to recover time-variable gravity (TVG) and realize the terrestrial reference frame (TRF) using all available data from the GRACE missions and a global network of terrestrial GPS stations. Laying the groundwork for this approach are recent results demonstrating that GRACE can be powerfully exploited as an orbiting fiducial laboratory to improve the accuracy of the TRF realized from GPS alone. The rapidly moving baselines formed between ground stations and GRACE dramatically improve the spatial and temporal diversity of the global geodetic network, while also subverting systematic errors linked to the repeating geometries of the GPS orbital planes. We expect that this approach will enable improved separation of low-degree gravity variations and the TRF, enabling better recovery of geocenter motions and promoting long-term stability in the frame.

Enabled by the development of new capabilities in our modernized (GipsyX) software, elements of our strategy are described in this poster. They include: 1) simultaneous reduction of GPS data from GRACE and a global network of ground stations; 2) incorporation of data from the GRACE inter-satellite (K-band) link as biased-range (carrier-phase) measurements; 3) incorporation of GRACE accelerometer data to accommodate non-conservative errors; 4) application of a new solar radiation pressure model for the GPS satellites that is independent of any underlying TRF definition; 5) resolution of carrier-phase ambiguities in a new adaptive approach that takes better advantage of links to the GRACE satellites; 6) inclusion of geopotential coefficients and Earth orientation parameters in a grand “fiducial-free” solution, wherein the coordinates for all GPS and GRACE satellites and ground stations are estimated simultaneously. We describe results from test implementations of this strategy, and outline our plans to develop an extended time series of solutions spanning the GRACE mission.

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Poster Title: Multiresolution analysis of GRACE range rate residuals
Presenter: Goswami, Sujata
Co-Authors: S. Behzadpour, T. Mayer-Gürr, J. Flury

Abstract: The level of postfit residuals in the temporal gravity field determination using GRACE observations considerably exceed the expected level of sensor noise. This results in an ongoing effort to understand the error content of observations, as well as any inaccuracy in the physical and stochastic models. The main challenge in the residual analysis is that several noisy signals and disturbances are known to be superimposed at each frequency. More importantly, the analysis is based on the assumption of stationary behavior of these signals. However, in reality most of these signals have nonstationary behavior, meaning that they have dynamic frequency components over time. In an attempt to consider the time variation, time-frequency methods can be applied to identify and localize each component of the residuals in time for further statistical, spatial, or orbital analyses. Among these methods, the Discrete Wavelet Transform (DWT) is of particular interest for analysis of non-stationary and transient time series.

In this work, the Multi-Resolution Analysis (MRA) using DWT is applied to decompose the range rate residuals into different frequency bands at different scales which more clearly represents previously known or unknown underlying errors in measurements and physical models. This study also provides an opportunity to improve the stochastic model and the accuracy of the GRACE parameter estimation , as well as its successor, GRACE Follow-on.

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Poster Title: Improved GRACE accelerometer data transplant due to thruster spike modeling
Presenter: Bandikova, Tamara
Co-Authors: C. McCullough, G. Kruizinga

Abstract: Since September 2016, the accelerometer (ACC) onboard GRACE-B has been turned off in order to reduce battery load. The missing GRACE-B accelerometer data, however, can be recovered from the GRACE-A accelerometer measurement with satisfactory accuracy. In the current GRACE data processing, ACC data transplant includes only attitude and time correction. Here we present an improved ACC data transplant which in addition includes modeling of residual linear accelerations due to thruster firings. These residual linear accelerations (‘thruster spikes’) are one of the most dominant high-frequency signals in the ACC measurement and are caused by thruster imperfections such as misalignment of thruster pair, force imbalance or differences in reaction time. Modeling of the thruster spikes for both GRACE-A and GRACE-B results in significantly improved accuracy of the transplanted data.

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