A.1.1 to A.1.11 - Analysis
(Convener: )

Twangs: Model Parameters, Spatial Correlation and Possible Causes - a Summary
(N. Peterseim, A. Schlicht, J. Flury)

Analysis of attitude errors in GRACE data and their impact on monthly gravity field models
(P. Inacio, P.Ditmar, R.Klees)

Simulations of the Ocean Calibration Approach for Correcting for Spurious Accelerations
(P. L. Bender, C. R. Betts)

Toward a Release-06 of GRACE Atmosphere and Ocean De-Aliasing Level-1B (AOD1B) Product
(E. Fagiolini, F. Flechtner, H. Dobslaw, I. Bergmann-Wolf, J. Kuhlmann)

Release 3 of the GRACE gravity solutions from CNES/GRGS
(J.M. Lemoine, S. Bourgogne, S. Bruinsma, P. Gegout, R. Biancale)

JPL RL05M Constrained Mascon Solution: Strategy, Evaluation, and Status
(D. Wiese, M. Watkins, D. Yuan, C. Boening, F. W. Landerer)

A new global mascon solution product
(S. Luthcke, B. Loomis, T. Sabaka, D. Rowlands)

Dectecting regional scale water mass variations with GRACE
(E. Fagiolini, Ch. Gruber, Ch. Dahle, F. Flechtner)

Kalman filtering for statistically rigorous separation of geophysical signal and stripe noise in decade-long GRACE solutions
(W. Lei, J. L. Davis, E. M. HIll, M. E. Tamisiea, K. A. Macpherson)

Optimized signal denoising and mass balance estimates of GRACE-like mass change time series
(B. Loomis, S.B. Luthcke)

A Modified Short Arc Approach for Recovering Gravity Field Model
(S. Yunzhong, Q. Chen, H. Hsu, X. Zhang, L. Lizhi)

Impact of self-attraction and loading on degree 1 estimates for GRACE
(K. Quinn)

Time variability of GRACE data using JPL mascons
(B. Killett, V. Zlotnicki, D. Wiese, M. Watkins)

Title: Twangs: Model Parameters, Spatial Correlation and Possible Causes - a Summary
Presenter: Peterseim, Nadja
Co-Authors: N. Peterseim; A. Schlicht; J. Flury

Abstract: In our study we focus on the hitherto not clearly resolved issue called twangs in the 10 Hz accelerometer data (ACC1A) of GRACE. We will show how twangs can be identified and extracted from data, and how a model can be retrieved upon the extracted twangs by means of a Gaussian reconstruction filter and a parameter based LSA. Based from this model, we can give an outlook on the possible influences on Level 1B accelerometer data (ACC1B). Furthermore, a great majority twangs can be spatially correlated to the environment of the spacecraft in terms of season, local time, solar impact and albedo, i.e. terrestrial thermal radiation. Other twangs may be directly linked to a starting or ending input current of the solar arrays of the GRACE satellites.

A variety of these observations contradict the popular hypothesis that twangs may be cause by vibrations of the multi-layer insulation. In contrast, they support the hypothesis that twangs may be evoked by a discharging phenomena of the satellite planes, which are getting charged surrounding plasma at spacecraft altitude.

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Title: Analysis of attitude errors in GRACE data and their impact on monthly gravity field models
Presenter: Inacio, Pedro
Co-Authors: P. Inacio; P.Ditmar; R.Klees

Abstract: Each GRACE satellite makes use of two star cameras for the precise measurement of the spacecraft's attitude in the Celestial Reference Frame. In the context of gravity field modelling, the spacecraft's attitudes are needed i) to provide the orientation of the non-gravitational forces acting on the satellite, which are measured with onboard accelerometers; ii) to compute the 3-D offset between the GPS antenna and the satellite's centre of mass (CoM); and iii) to compute the 3-D offset between the K-Band antenna phase centre and the CoM. The latest release of Level-1B GRACE data (RL02) make use of improved satellite attitude products in which star camera (SCA) biases have been eliminated. However, a detailed investigation of remaining SCA errors their propagation into monthly gravity field models has not been done yet.

The presence of two (primary and secondary) SCAs on each satellite creates a redundancy in the measurement of satellite attitudes. Differences between primary and secondary SCA data are interpreted as noise realizations of the attitude determination system. They show two distinct error components: a deterministic component, highly correlated with the satellite's true anomaly, and a stochastic component. We compute comprehensive models that accurately describe each component. This allows realistic realizations of SCA noise to be generated. These noise realizations are propagated into inter-satellite accelerations and analysed in the spectral domain.. We show that SCA noise may provide a significant contribution to the overall error budget in inter-satellite accelerations. In the frequency range 3-10 mHz, for instance, SCA errors may become comparable with the total noise observed in GRACE inter-satellite accelerations. Furthermore, SCA noise is propagated into monthly gravity field solutions and is compared with estimates of noise in GRACE data.

In addition, we demonstrate that the mutual configuration of SCA and K-band antenna on board GRACE satellites does not allow the full accuracy of the SCA assembly to be exploited in gravity field recovery. This observation is particularly relevant for future satellite gravity missions, in which inter-satellite ranges will be measured with laser interferometers to achieve a higher accuracy of gravity field determination, as compared to GRACE. In order to benefit from a high performance of these sensors, it is indispensable to improve the accuracy of satellite attitude determination.

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Title: Simulations of the Ocean Calibration Approach for Correcting for Spurious Accelerations
Presenter: Bender, Peter L
Co-Authors: P. L. Bender; C. R. Betts

Abstract: We have simulated a new method for correcting for spurious accelerations of the spacecraft for about half of the time during the GRACE Follow-On mission. This method makes use of data during periods of 4 successive revolutions when the ground tracks are crossing the central Pacific. Measurements of the satellite separation S(t) at preferred calibration points are compared with the geopotential height variations at altitude at these sites based on ocean model information. Corrections for the spurious differential accelerations are then interpolated during the roughly 6 hr period of the 4 revolutions.

Our calibration points are mainly the locations during the 4 revolutions when the orbits cross -30, 0, and +30 deg lat in the central Pacific. However, the 5 crossing points over the south pole would be included also, and usually 1 point each near the equator in the Indian and Atlantic Oceans. In our simulations we have used a model for the uncertainties in the geopotential heights that is based mainly on the ECCO-JPL model for ocean bottom pressure variations in the Pacific, as discussed below. For the south pole, the mean uncertainty is expected to be large, but the variations during the roughly 6 hr period are assumed to be small.

For the ECCO-JPL model, we have compared the ocean bottom pressure (OBP) results every 12 hours during Dec., 2010, at 15 sites with the results at nearby OBP sensors of the DART network. The sites are located between -33 and +33 deg in lat and 146 and 274 deg E long. The rms variations in water height over the 15 DART sites was 1.6 cm, and the corresponding variations at the nearby ECCO sites was 0.9 cm. The correlation coefficients ranged from 0.38 to 0.85, with a mean of 0.47.

Based mainly on the ECCO model, we have developed the following model for the geopotential height variation uncertainties at satellite altitude over the calibration sites in the Pacific: 2 mm random uncertainties at each site plus a common 2 mm uncertainty at all of them; and 1.5 mm uncertainties in the N-S and E-W gradients across the whole area. With this model, our simulations indicate that the errors for the roughly 6 hr periods will be roughly 5 mm, including both the limitations due to the interpolation process and the geopotential height uncertainties at the calibration sites.

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Title: Toward a Release-06 of GRACE Atmosphere and Ocean De-Aliasing Level-1B (AOD1B) Product
Presenter: Fagiolini, Elisa
Co-Authors: F. Flechtner; H. Dobslaw; I. Bergmann-Wolf; J. Kuhlmann

Abstract: An updated version of the OMCT ocean model with 1° spatial resolution provides bottom pressure anomalies for the latest Release-05 of the GRACE Atmosphere and Ocean De-aliasing Level 1B (AOD1B) product. For high-frequency signals with periods below 30 days, this model reduces the root-mean-square of residual sea level variability seen by ENVISAT by 2 cm in large parts of the extra-tropical oceanic areas, which corresponds to about 50% of the total signal in open ocean regions away from the western boundaries. Comparable residual reductions are also obtained with respect to both in-situ ocean bottom pressure data and GRACE KBRR measurements, thereby outperforming all previous versions of AOD1B.

In this contribution, we present results from a number of experiments performed to further improve the quality of AOD1B in preparation for a potential future new release of GRACE gravity fields. This includes, for the atmospheric part: an improved 3D algorithm, the consideration of ERA Interim re-analysis data, and at the same time the possibility of correcting the operational data from spurious jumps (e.g. in 2006 and 2010). In the OMCT ocean simulations part we investigate the explicit consideration of self-attraction and loading of the water masses on the ocean dynamics and the use of updated bathymetry information in various coastal regions including the Arctic.

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Title: Release 3 of the GRACE gravity solutions from CNES/GRGS
Presenter: Bourgogne, Stephane
Co-Authors: J.M. Lemoine; S. Bourgogne; S. Bruinsma; P. Gegout; R. Biancale

Abstract: The GRACE mission, already more than 10 years in operation, has provided a large-scale vision of the temporal gravity variations occurring on the Earth's surface.

Since the complete reprocessing of the Level-1B data ("V2") by JPL, a new reprocessing of the Level-2 data has been made available to the public: RL05, from CSR, GFZ and JPL. In this context the CNES/GRGS team has undertaken a full reiteration of the GRACE and LAGEOS data processing based on upgraded data, models and inversion procedures, leading to CNES/GRGS release 3 or "RL03".This new release of the CNES/GRGS GRACE gravity solution features, in addition to using the L1B-V2 data:

• an improved a priori gravity model, closely following the actual gravity variations already observed by GRACE,
• the use of FES2012 tide model in replacement of FES2004,
• the use of the atmospheric dealiasing fields ECMWF ERA-interim (every 3 hours) in re- placement of ECMWF operational model (every 6 hours),
• the use of the oceanic dealiasing fields TUGO (every 3 hours) in replacement of MOG2D (every 6 hours),
• some changes in the K-Band ranging and accelerometer parameterization,
• an inversion procedure using truncated Eigen values allowing, as was the case for RL02, a direct interpretation of the gravity solutions without the need for additional filtering,
• an extension of the maximal degree of the time-variable parameters from 50 to 80.

The processing of the CNES/GRGS RL03 arcs has been completed. The current step is the production of a new mean field, as a necessary prerequisite for monthly and 10-day solutions. SVD inversion strategy has been adopted, although some issues are still currently under study. Along with 10-day solutions, we will also deliver monthly solutions with very little stabilization in order to be directly comparable with other groups, and to allow analysis at maximum resolution.

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Title: JPL RL05M Constrained Mascon Solution: Strategy, Evaluation, and Status
Presenter: Wiese, David
Co-Authors: M. Watkins; D. Yuan; C. Boening; F. W. Landerer

Abstract: The majority of the GRACE gravity solutions released to date have been obtained by fitting the data to spherical harmonic basis functions without apriori-conditioning of the solution. The resultant products are contaminated with longitudinal stripes, which are typically removed via empirical post-processing filters. JPL has developed a new solution strategy using spherical cap mass concentration blocks ('mascons') as the basis function and variance information derived from geophysical models to place realistic constraints on the solution. These solutions are therefore more "optimally" destriped than purely empirical posteriori filters. We compare the conditioned mascon solutions to RL05 spherical harmonic solutions and summarize key global mass flux results for cryosphere, hydrology, and ocean applications. Several advantages of using the mascon solutions over harmonics are discussed.

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Title: A new global mascon solution product
Presenter: Luthcke, Scott
Co-Authors: B. Loomis, T. Sabaka, D. Rowlands

Abstract: A new global mascon solution of the Earth's surface mass redistribution, estimated from a decade of GRACE observations, is now publically available. The solution is estimated directly from the reduction of the GRACE L1B RL2 data taking into account the full noise covariance, and formally iterating the solution. The new solution increases signal recovery while reducing the GRACE KBRR observation residuals. The mascons are estimated with 10-day and 1-arc-degree equal area sampling, applying anisotropic constraints for enhanced temporal and spatial resolution of the recovered land ice signal. This latest solution uses the most recent IERS2010 models and standards and is distributed in a fully documented hdf5 format. The new product includes the estimated signal for each mascon, the optimally filtered signal with noise removed, a set of signal characterization parameters, and calibrated errors of the 10-day solutions and mascon trends. In addition the new product also contains the forward models used in the estimation process, as well as additional information/corrections supplied in the same mascon format as the solution itself. This presentation provides the details of the new global mascon solution, the product details and access, as well as examples of the application of this product to ice mass balance and hydrology research.

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Title: Dectecting regional scale water mass variations with GRACE
Presenter: Fagiolini, Elisa
Co-Authors: Ch. Gruber; Ch. Dahle; F. Flechtner

Abstract: One of the key signals of the time variable gravity field measured by the GRACE mission is the continental hydrological cycle. Since GRACE is measuring globally and continuously, it is particularly suitable to identify, monitor and model surface and ground water mass changes. Global gravity field spherical harmonic solutions, recently reprocessed by GFZ (RL05), based on global spherical harmonic coefficients (SHC), are suitable to monitor interaction of mass changes at large scale and have reached very good quality showing significantly less noise and spurious artifacts. However, they suffer from many deficiencies such as limited spatial and temporal resolution, restriction to monthly availability with about two months delay, necessary post-filtering of the spherical harmonic coefficients to correct noise amplification (stripes) before estimating water mass changes. This kind of post-filtering amplifies the so-called "leakage" effect described as signals spreading out from their corresponding sources (e.g. rivers). On regional-scales, water mass changes from different sources interfere with each other resulting in superimposed fictitious signals that can be easily misinterpreted. Compensating for leakage effects requires an additional post-processing fitted to specific time and location, thus introducing further constraints and uncertainties.

In order to focus towards higher spatial and temporal resolution, new data processing methods such local inversion by integral kernel functions and Kalman filtering have been widely studied, developed and implemented. These new methods discovered high potentiality of GRACE in detecting high-frequency temporal and spatial events such as regional water variations over specific river basins avoiding the use of post-filters. We expect global and regional hydrological models and sparse ground-based measurements to profit from such accurate outcomes. We present and discuss first results obtained at GFZ comparing the "alternative" mass changes observed with GRACE with hydrological simulations for several catchments such as spatially explicit hydraulic simulations of the large scale annual inundation volume during the flood season in the Mekong Delta.

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Title: Kalman filtering for statistically rigorous separation of geophysical signal and stripe noise in decade-long GRACE solutions
Presenter: Lei, Wang
Co-Authors: J. L. Davis; E. M. HIll; M. E. Tamisiea; K. A. Macpherson

Abstract: Original GRACE data are contaminated by errors manifesting themselves as north-south elongated linear stripes in maps of surface mass changes. Swenson and Wahr [2006] noted that these stripe features are associated with correlated errors in the spherical harmonic coefficients, and designed a destriping process to successfully reduce the stripe features. However, this typical destriping process is an ad-hoc method and doesn't allow for estimation of post-destriped covariances. In this study, we introduce a Kalman filter method which is developed for statistically rigorous separation of geophysical signals and stripes noise. In contrast with the ad-hoc method, we model both the stripe noise and temporal variability in geophysical signals as stochastic processes and thus enable the destriping process to be performed in a Bayesian framework. The Kalman filter is applied to decade-long GRACE monthly gravity field series, and the results demonstrate that the new method is able to suppress the stripe noise more effectively. Since this new destriping method is performed in the Bayesian context, we can propagate robust covariance matrices reflecting the correlated errors and the impact of the removal process. In addition, spatial Gaussian smoothing is not required as the Bayesian approach yields a natural resolution for the geophysical signal, reflecting the correlated errors. This approach is therefore an appropriate "front-end" for the more statistically rigorous and self-consistent modeling of seasonal and longer-term signals, and the statistical techniques recently developed to combine GRACE and other data for simultaneous estimation of glacial isostatic adjustment and present-day melting signals.

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Title: Optimized signal denoising and mass balance estimates of GRACE-like mass change time series
Presenter: Loomis, Bryant
Co-Authors: B. Loomis; S.B. Luthcke

Abstract: An extensive simulation study was performed on GRACE-like regional mass change signals in an effort to identify effective methods for signal denoising and the estimation of seasonal timing and mass balances. This work is motivated by the desire to extract the times that mark the beginning of the mass accumulation and loss seasons and the corresponding net balances in cryospheric regions using the time series of land ice mass change available from the recent NASA GSFC global mascon product. For the purpose of signal denoising, we tested the following algorithms: Gaussian smoothing, wavelet thresholding, ensemble empirical model decomposition (EEMD), complete EEMD with adaptive noise (CEEMDAN), and Wiener filtering. For the isolation of the seasonal signal, we apply and analyze the following methods: wavelet multiresolution analysis, EEMD, CEEMDAN, and a newly-developed cluster analysis of the intrinsic mode functions generated by the EEMD and CEEMDAN algorithms. For signal denoising we achieve the best results with a Wiener filter, where the signal spectrum is approximated with the Gaussian smoothed signal, and the noise level is approximated with the highest frequency wavelet coefficients. The optimal approach for the isolation of the seasonal signal and corresponding estimation of mass balances is the cluster analysis enhancement of the CEEMDAN method. We also show that this new method provides reliable uncertainties of the estimated parameters.

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Title: A Modified Short Arc Approach for Recovering Gravity Field Model
Presenter: Yunzhong, Shen
Co-Authors: S. Yunzhong; Q. Chen; H. Hsu; X. Zhang; L. lizhi

Abstract: In computing the force attracting on low Earth orbit satellite, one needs to use the satellite's position vector, which is integrated from the satellite initial state vector and a prior for model in dynamical approach, or uses the kinematic orbit after gradient correction in short arc approach. However, in our modified short arc approach, the kinematic orbit in force model is treated as pseudo observation, and its observation error and the range rate observation error are modeled together with the parameters including the harmonic coefficients of gravity field model and the bias parameters of acceleration measurements in the same observational equation. The observation equation is solved based on weighted least squares adjustment by minimizing both pseudo orbit observation error and the range rate observation error. In our modified approach, the initial state parameters and prior gravity field model are not needed. By using the real GRACE orbits, the range rate and acceleration measurements officially released by JPL (Jet Propulsion Laboratory), we have computed the monthly gravity field model series from Jan. 2003 to Aug. 2011 complete to degree and order 60. In our solutions, the short arc length is 2 hours and three bias parameters (along, cross and radial) are set up for one hour arc. By comparing the degree geoid errors of our model with the RL05 models released respectively by CSR (Centre for Space Research), JPL and GFZ (GeoForschungsZentrum), we show that our solution is as accurate as the released RL05 models.

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Title: Impact of self-attraction and loading on degree 1 estimates for GRACE
Presenter: Quinn, Katherine
Co-Authors: K. Quinn

Abstract: GRACE gravity data, being in a center of mass reference frame, are insensitive to degree 1 variations.  To be consistent with other observations and models of surface mass variations, the GRACE data need to be translated into a center of figure reference frame by adding estimates of degree 1 coefficients.  The most widely used degree 1 estimates are derived from a combination of degree 2 and higher GRACE gravity coefficients and ocean model estimates of the degree 1 variability, as described by Swenson et al. [2008].  They assume that spatial variations in ocean mass can be estimated from ocean models while the total ocean mass variations can be estimated from GRACE and an initial estimate of seasonal degree 1 variations from satellite laser ranging observations.  The total ocean mass variations are added as a uniform layer over the ocean.  However, gravitational self-attraction and loading effects (SAL) are known to cause spatially non-uniform ocean mass variations related to changing land hydrology, atmospheric pressure, and ocean dynamics mass loads. We propose to refine the Swenson et al. [2008] degree 1 estimates by accounting for SAL.  Experiments using synthetic data constructed from land hydrology, atmosphere, and ocean models indicate that adding SAL could change the degree 1 variance by ~4%. However these synthetic tests did not include secular mass load changes in Greenland and Antarctica, which may result in significant changes in the degree 1 estimates. We also intend to show preliminary results using actual GRACE data.

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Title: Time variability of GRACE data using JPL mascons
Presenter: Killett, Bryan
Co-Authors: B. Killett; V. Zlotnicki; D. Wiese; M. Watkins

Abstract: The time variability of the new JPL mascon GRACE solutions is characterized on multiple time scales. Their power spectra are mapped onto the visible spectrum of light, following the approach in Hughes and Williams 2010. These spectra are compared to those from the Noah land hydrology model in the Global Land Data Assimilation System (GLDAS). Characterizing temporal correlations leads to a rigorous calculation of the statistical significance of mass trends.

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