A.1 + A.3 - Analysis Scatter / Processing Techniques
(Moderator: Frank Flechtner)


   Richard Biancale (10)
   Kevin Fleming (10)
   Frank Lemoine (10)
   Ingo Sasgen (5)
   Ernst Schrama (10)
   Bjoern Frommknecht (10)
   Shin-Chan Han (10)
   Frank Lemoine (10)
   Xiaoping Wu (10)
   Discussion (5)


Richard Biancale (10)
Presenter: Richard Biancale
Co-Authors: , J.-M. Lemoine, S Loyer, S. Bruinsma, F. Perosanz, G. Balmino
Title: GRACE data processing in CNES/GRGS; results and discussion

Abstract: In the framework of the space gravimetry activities the CNES Team of Space Geodesy delivers on a regular basis geoid products based on GRACE and LAGEOS data. These products span now a 4 years period (mid-2002-mid 2006) at 10-day resolution. The GRACE-LAGEOS combination allows us to determine the temporal variations of the gravity field from degree 1 to degree 50, although degrees 30 to 50 are stabilized toward a mean model. Some details on data processing and model stabilization are presented and comparisons with other models are shown.

Studies using these models can be performed without any additional filtering process (although some small artifacts are still present). So seasonal and linear variations in water mass storage, big earthquake seismic and post-seismic deformations are showed as example of such studies.

Moreover, we discuss new investigations in order to improve results

On the other hand, accelerometer data should help for modelling thermosphere densities. However, for that purpose, level-1a data would be better appropriate than regularized level-1b data. We propose to discuss this point as well.


Kevin Fleming (10)
Presenter: Kevin Fleming
Co-Authors: I. Sasgen, Z. Martinec
Title: Statistical analyzes and comparisons of inferred temporal trends in the GRACE gravity field solutions

Abstract: Since its launch in March 2002, the Gravity Recovery and Climate Experiment (GRACE) space mission has provided around 4 years of monthly-average gravity-field solutions. These solutions are made available to the scientific community via a series of releases independently produced by the GRACE Science Data Service (SDS) centers and other institutions. Each release represents the state of that center's optimal processing methodologies. The problem for "users" is therefore deciding which release or releases are the most appropriate to their needs.

This work discusses an assessment of the temporal trends in the terrestrial gravity field as inferred from several GRACE releases. We compare four releases: RL01 from the Center for Space Research (CSR), RL03 from the GeoForschungsZentrum (GFZ), RL02 from the Jet Propulsion Laboratory (JPL), and a release from the Centre d'Etudes Spatiales (CNES). Temporal variability in the terrestrial gravity field is identified by fitting a 6-parameter model consisting of an offset, secular and annual and semi-annual sine and cosine terms to the time series of the Stokes potential coefficients that make up the solutions, a procedure in common with many GRACE-related works. Based on the analysis of the resulting residuals, we then assess: 1) the statistical reliability of the inferred terms, making use of the Students t-test for the secular terms, and the Fisher F-test for the periodic terms, 2) the assumption of the homogeneity of the variances and the normal distribution of the data. The resulting temporal trends associated with each release are then discussed, paying attention to the discrepancies that may arise in interpreting the results.


Frank Lemoine (10)
Presenter: Frank Lemoine
Co-Authors: S. B. Luthcke, D. D. Rowlands, D. S. Chinn, S. M. Klosko
Title: Signal Analysis of GRACE solutions

The GRACE Science Team has produced Level2 Science Products, monthly spherical harmonic solutions, using a variety of processing strategies. In this paper, we analyze the monthly solutions from UT/CSR (RL01), GFZ (RL03), and NASA GSFC (V03B). We perform a signal analysis on each dataset after converting the harmonics to grids of estimated water height. We calculate the annual, semiannual, and tidal S2 signal amplitudes, the linear trend apparent using the monthly grids. In addition, we characterize the residual noise in each solution by examining the signal exclusively over arid regions, and the ocean basins. We also examine the solution degree amplitudes for the three sets of solutions. Our intent is to characterize and compare and contrast the differences in the various sets of solutions.


Ingo Sasgen (5)
Presenter: Ingo Sasgen
Co-Authors: Z. Martinec; K. Fleming
Title: Wiener optimal combination and evaluation of GRACE gravity fields over Antarctica

Abstract: We present an appraisal method for the Gravity Recovery and Climate Experiment (GRACE) gravity-field releases based on the Wiener optimal evaluation approach. The Wiener optimal evaluation uses linear convolution filtering and the subsequent addition of multiple inputs to minimize (in a least-squares sense) the difference between the combined optimal output and a desired output. Investigating the individual filtered outputs with respect to the desired output provides a measure of the quality of each input. Here, the inputs are linear trends of the gravity-field change over Antarctica inferred from the Stokes potential coefficients of the 4 independent GRACE releases; GFZ RL03, CSR RL01C, JPL RL01C and CNES RL01C, each with at least 27 months worth of data. The desired output is based on the predicted gravity-field change over Antarctica resulting from by present-day ice-mass changes and ongoing glacial-isostatic adjustment (GIA). We demonstrate that the combined output of the Wiener optimal evaluator improves the quality of the signal over Antarctica with regards to the desired output. We show that 3 of the 4 GRACE releases essentially constitute the desired signal in the optimal combination, while one mainly reduces the contaminating noise over the oceans. The best agreement with the predicted gravity-field change over Antarctica is represented by the release CNES RL01C.


Ernst Schrama (10)
Presenter: Ernst Schrama
Title: Signal and noise in GRACE observed surface mass variations

Abstract: The GRACE product used for this study consists of 43 monthly potential coefficient sets released by the GRACE science team that are used to generate grids with equivalent water heights (EQWHs). We optimized both the smoothing radius and the level of approximation by EOFs and found that 7.5 degree and 6 modes are able to describe more than 75% of the variance of the GRACE observed equivalent water height grids. The recovered surface mass signal describes all known variations in the continental hydrology, a Greenland ice change mode and possibly two other modes that resemble interannual effects, although the existence of these modes is not confirmed by a GPS calibration experiment. To assess the quality of the estimated grids we constructed degree error spectra of equivalent water heights. We conclude that a significant part of the present error structure in GRACE can be explained by a scaling factor of 1.08 relative to degree errors estimates provided by the GRACE team. The comparison of degree error spectra is a valuable tool if the GRACE error looks like a homogeneous and isotropic function, yet we found that more information can be retrieved from the full covariance matrix. To validate the spatial structure of the EQWH signal we introduce a signal to noise ratio (SNR) function to interpret the local sensitivity of the GRACE system. The SNR function depends both on the EQWH signal variance and on the formal error covariance of the GRACE gravity product. We show four examples where the SNR function is used to classify observability of the surface mass signal.


Bjoern Frommknecht (10)
Presenter: Bjoern Frommknecht
Co-Authors: U.Meyer; R. Schmidt;
Title: Integrated Sensor Analysis for GRACE - L1a K-Band processing

Abstract: The performance of the current GRACE gravity field models significantly exceeds the performance of all other models available before GRACE. However, the performance of these new models is still below the predicted performance. This degradation in performance has a strong effect on the geophysical exploitation of the GRACE mission. There are two possible causes for the degraded performance:

  1. It is possible that the analysis models are simply not sophisticated enough for fully exploiting the information content of the gravity field sensor system. There could also be deficiencies in the accuracy and the consistency of the used geophysical reduction models or the gravity field determination algorithms.
  2. The second possible explanation is that the accuracy of individual elements or of the interaction of the individual elements of the gravity field sensor system is suboptimal or that inadequate signal processing methods have been used.

The purpose of this investigation is a thorough analysis of this second complex.

The Jet Propulsion Laboratory in Pasadena is entrusted with the operational GRACE data processing. In this talk, the results of the review of the applied processing strategy from the level of raw instrument data (level 1a) to the level of gravity field determination input data (level 1b) for the K-Band Data will be presented. Possible alternatives to the official processing strategy will be discussed and occurring differences will be evaluated in terms of the expected impact on the derived gravity field models.


Shin-Chan Han (10)
Presenter: Shin-Chan Han
Co-Authors: C. Jekeli; C. Shum
Title: Localized analysis of GRACE L1B and L2 data products for validating time-variable gravity

Abstract: We summarize two methods to estimate the geographically-confined and time-variable gravity with optimal resolution and accuracy. In the first method, the L1B data product is re-analyzed to construct the in situ gravitational potential difference at altitude and subsequently the downward-continuation is performed to model the regional, time-variable gravity. The demonstrated higher temporal resolution in this method yields the detection of sub-monthly gravity changes (e.g., M2 aliased tides). The higher spatial resolution provides enhanced spatial description of the mass (re-)distribution. The second method is on the basis of localizing the monthly L2 data product. The result from localization of global harmonic coefficients was attained with the similar spatial resolution as the one processed in the first method, although the temporal resolution of the second method is still limited to one month. We discuss some proposed innovations to the algorithm in order to achieve ultimately seamless, unified and improved global solution from all regional patches.


Frank Lemoine (10)
Presenter: Frank Lemoine
Co-Authors: S. B. Luthcke, D.D. Rowlands, S.M. Klosko, D.S. Chinn, J.J. McCarthy
Title: Unique Approaches to Time-Variable Gravity from GRACE: Investigation Status

Abstract: In our investigation, we have focused on enhancing the time-variable gravity recovery from GRACE by applying unique approaches to the reduction of the GRACE K Band Range-Rate (KBRR) data, and subsequent time-variable gravity solutions. Our regional gravity solutions have enabled the economical recovery of time-variable gravity. We have developed significant advancements to the GRACE analysis approaches by exploiting these data to extract the ~300 km spatial and 10-day temporal resolution inherent in the KBRR data. This has been accomplished using mascons or mass concentrations. Our special techniques include (1) the parsimonious parameterization of accelerometer biases; (2) The use of only the KBRR data in our solutions; (3) the use of the project-produced precise GPS trajectories; and (4) the use of a reduced special state vector estimation scheme for the GRACE satellites. In this paper, we summarize the status of investigation and describe products derived from analysis of three years of GRACE data, from July 2003 to July 2006, which include the regional solutions for South America, the Mississippi Basin, India, the polar regions, as well as those for global spherical harmonics.


Xiaoping Wu (10)
Presenter: Xiaoping Wu
Co-Authors:
Title: Inverse and Probabilistic Methods to Filter GRACE Data for Geophysical Applications

Abstract: The GRACE gravity mission marks an important transition from local and component measurements to global accurate monitoring of surface mass variations. To map the satellite gravity data into average values of surface mass variation over a global grid and geographic regions, one has to contemplate the unique characteristics of the spherical harmonic error spectrum with strong degree and order dependences and non-negligent cross-correlations. We use continuous geophysical inverse methods to construct unimodular and optimal averaging kernels for point geoid height or mass variation values on the surface of the Earth. The kernel is much sharper than the Gaussian kernel with the same uncertainty. Similarly, with the same level of resolution, the optimal average has significantly higher accuracy than the Gaussian average. With efficient algorithms, the methods can be applied to fine global grids and cases of non-diagonal covariance matrices. Probabilistic methods using more realistic a priori information and unimodular optimal regional kernels will also be discussed.]

Discussion (5)


A.2 - GRACE Follow-On (Moderator: Mike Watkins)
   Michael Watkins (12)
   Erik Ivins (12)
   Jay Famiglietti (12)
   Ming Fang (12)
   C. K. Shum (12)
   Michelle Stephens (12)
   Peter L. Bender (10)
   Discussion (8)

Michael Watkins (12)
Presenter: Michael Watkins
Co-Authors: W.M. Folkner, R. S. Nerem, B. D. Tapley
Title: Top Level Issues for the GRACE Follow-On Mission

Abstract: NASA and the global science community are re-energized about continuing and improving the GRACE measurement series. We expect the Decadal Survey final report to reiterate and strengthen this view. In preparation for detailed discussion and proposals for new mission starts, we have begun a new round of mission architecture and error budget analysis, taking into account new developments learned from GRACE regarding aliasing effects, from the Instrument Incubator laser interferometer development, and recent developments in drag free technology. Wrapping all these technical issues are economic ones, including total mission cost and possible international partnerships. In this talk, we will summarize the trade space we will analyze on behalf of NASA, some early results, and the road map to get to a final community consensus architecture by mid-2007.


Erik Ivins (12)
Presenter: Erik Ivins
Co-Authors: Xiaoping Wu, Richard Gross and Victor Zlotnicki
Title: GRACE extended mission: An opportunity to test interannual ice mass change, PGR signature and other secular trends

Abstract: The GRACE gravity mapping product that has been available since the late spring of 2002 has provided a wealth of new data for studying hydrological and cryospheric sciences at a grand global scale. The new data allows interannual variability to be studied in depth. Clear signals are appearing at very long involving ocean mass variability and there are recent discoveries of clear post-glacial rebound (PGR) signals in the secular trends associated with the 3.5 years of gravity mapping. A number of questions are of concern to both the rebound community, in general, and to geodesists searching for non-rebound secular trends. The viscosity of the mantle is certainly one of these unresolved questions. However, where non-gravimetric near-field rebound data is available, such as high quality sea level curves from which exponential curve fits may be made which resolve (exclusively) the rheology of the upper mantle, the main science question that remains is a predominantly glaciological one: how big were the ice sheets at Last Glacial Maximum (LGM), 21 kyr BP, and how did they collapse?

Here we examine the secular trends of GRACE time series with the goal of ferreting out the localities and strengths of the time-dependent gravity signature associated with glacial mass loss from LGM and the transient solid Earth viscoelastic- memory response left in the wake of this deglaciation. The amplitude near the two main centers of late-Pleistocene ice sheets may be several mm/yr of change in geoid. Geoid change signatures caused by past loading events in areas where few in situ constraints exist are of great interest. These areas include parts of coastal East Antarctica, where ice sheet expansion is known to have occurred during the last 70,000 years, and the vast mountain plateaus of eastern Siberia where ice sheets are known to have existed during glacial climate epochs of the Late Pleistocene. However, it is clear from our analysis that improved hydrological and ocean tidal modeling may be important for comprehensive understanding of these secular signals. An extended mission may be crucial to detecting 'pure rebound' signal in Antarctica and Greenland.


Jay Famiglietti (12)
Presenter: Jay Famiglietti
Co-Authors: M. Rodell
Title: Why hydrology should support a GRACE follow-on mission

Abstract: The first 4 years of GRACE data have clearly demonstrated that the time-variable gravity signature on land is quite strong, and that it is dominated by terrestrial hydrology. As such, GRACE is providing a first-of-its-kind look at changes in terrestrial water storage. In this talk, I will review some recent work from our research team and from other groups that shows how the GRACE mission has enabled hydrologic applications that were not previously possible. These include the hydroclimatology and trends of terrestrial water storage, estimating continental and global freshwater discharge, global water mass balance, and remote sensing of groundwater. Results will be discussed, including current limitations, with implications for target improvements in a potential follow-on mission.


Ming Fang (12)
Presenter: Ming Fang
Co-Authors: C. Wunsch, B. H. Hager; R. Ponte
Title: On the Apparent Trend in Basin-Wide Water Storage Derived from GRACE

Abstract: A fundamental question of relevance to GRACE is whether a nine-year period of observation should be expected to yield a reliable estimate of secular trends in basin-wide water storage. The rate of water storage is the difference between the rates of mass gain by precipitation and mass loss by runoff and evaporation. We expect this rate of storage to be a function of climate forcing, while the storage variations to which GRACE is sensitive are an integrated response to climate forcing. As a simple illustration, suppose the system were forced by white noise alone. The resulting time integral would be a random walk, resulting in a finite trend in storage. The question is how the magnitude of this expected trend compares to the trends resulting from climate change or already observed via GRACE over the past several years. We address this question in the context of our recent inversion of GRACE data over Siberia for the three-year period, Jan. 2003 to Dec. 2005, which gives a negative trend in storage for the greater Ob watershed and a positive trend of nearly equal magnitude over the nearby Lena basin. We use 19-year long records (twice the period of hoped-for GRACE lifetime) of both precipitation rates and temperatures reported at a large number of gauging stations in the Ob and Lena regions to estimate the statistic character of the storage rates and the storage. These pseudo-storage rates are, in general, “colored” stochastic processes, modeled with Gaussian white noise forcing plus simple damping. These “colored” storage rates produce long lasting memory in the storage. Such processes have red spectrum character and are well-known to exhibit apparent trends over long time durations. In deed, significant apparent trends are found over times of 9 years, indicating that only very large climatic trends will be resolvable from the trends expected from stochastic forcing. Our results also suggest that at least a 20-year period is needed in order to distinguish between the apparent trends and the real physical trends.


C. K. Shum (12)
Presenter: C. K. Shum
Co-Authors: S.C. Han, M. Bevis, L. Wang, M. Watkins, R. Gross, D.N. Yuan, S. Nerem, S. Swenson, J. Wahr, Chen Ji, C.Y. Kuo, M. Schmidt, J. Freymueller, B.F. Chao, K. Cheng, C.W. Hwang
Title: Potential Coseismic Deformation Studies Using the GRACE Follow-on Mission

Abstract: It has been demonstrated that the GRACE satellites, equipped with microwave intersatellite ranging system, is capable of observing coseismic deformation in the form of gravity changes, even characterizing crust expansion (density change) resulting from a large undersea subduction earthquake (the Mw=9.2 December 2004 Sumatra-Andaman earthquake). With a laser interferometer proposed for the GRACE-follow on mission, which potentially has 50-100 times more sensitivity to coseismic (and post-seismic) deformations, there is a possibility that much smaller (Mw=8 or less) and more common earthquakes could be observable by spaceborne gravimetry sensors. This presentation describes a study for the feasibility of GRACE-II for observing and studying coseismic deformation of earthquakes with significantly smaller moment magnitude (e.g., the 2002 Mw=7.9 Denali earthquake) than the Sumatra-Andaman earthquake.


Michelle Stephens (12)
Presenter: Michelle Stephens
Co-Authors: R. S. Nerem, P. Bender, M. Watkins, B. Folkner, B. Loomis, R. Pierce, J. Leitch
Title: Development of an Interferometric Laser Ranging System for a Follow-On Gravity Mission to GRACE

Abstract: We report the results of an effort, supported by NASA’s Earth Science and Technology Office Instrument Incubator Program, to advance the technology of interferometric ranging in low Earth orbit. We have reduced risk for a follow-on gravity mission to GRACE by demonstrating performance of a heterodyne interferometric laser ranging instrument appropriate for a follow-on gravity mission to GRACE at the NASA Technology Readiness Level (TRL) 6, with traceability to the ranging error budget of a strawman flight design of the interferometric ranging system. Our strawman flight design and the driving terms in the error budget such as laser frequency noise, accelerometer noise, thermal effects, coupled wavefront distortion/pointing jitter effects, clock noise, and phase detection noise will be described. The overall performance of a GRACE follow-on mission will be limited at low frequencies by the accelerometer noise and at higher frequencies by the laser frequency noise. Control of those noise sources was not included in this effort. Our project goal was to ensure that all other ranging error sources related to the optical interferometry are less than the expected noise from the laser and the accelerometer.

We report on the performance of a flight-like engineering unit of the interferometric laser-ranging instrument. The on-orbit interferometric instrument would include two 1.06 um frequency-stabilized lasers, phase meters capable of precision heterodyne phase measurement in the presence of large Doppler shifts, and a quadrant photodiode for detection of both the range rate and spacecraft pointing offsets through measurement of phase differences between the quadrants. Our flight-like engineering unit includes an optical fiber launch (light from the laser is coupled onto the optical bench via an optical fiber), a low-noise quadrant photodiode and amplifier, a low-distortion telescope, polarization optics, a precision phasemeter designed, built and supplied to by JPL, and a simulated proof-mass. It does not include a frequency-stabilized laser.

The instrument optical bench and photodetector assembly are designed to undergo thermal and vibration testing to ensure space-flight readiness. A model has successfully completed vibration and non-operational thermal testing. The optical bench is less than 0.1 m x 0.1 m and weighs less than 10 kg. The single refractive telescope is used to both transmit the light from the local spacecraft and to receive light from the distant spacecraft. Manufacturing processes and optical components that are flight-qualifiable have been demonstrated. The telescope body and bench are Zerodur, while most of the remaining optics are fused silica.

An earlier, non-flightlike version has demonstrated laser ranging performance over laboratory distances near the 1 nm/sqrt(Hz) level.


Peter L. Bender (10)
Presenter: Peter L. Bender
Co-Authors: John L. Hall
Title: Flight-Compatible Laser Stabilization Cavity

Abstract: There has been success recently in mounting laser stabilization cavities in such a way that they have considerably reduced sensitivity to vibrations. However, these cavity-mounting methods were designed for laboratory use. For applications in space, the environment usually will be much more quiet, but the apparatus has to survive a high level of vibration during launch. In addition, the test stand environment during laser system qualification, integration and testing may be substantially worse than a quiet laboratory environment.

To partially overcome the flight-compatibility problem, a pair of 100 mm long Fabry-Perot cavities with 30 mm o.d. spacers and 70 mm o.d. outer support cylinders have been designed and are now under construction. The spacer is connected to the support cylinder by a 5 mm thick disk near the middle of the spacer. The structure is being machined from a single cylinder of ULE, in order to have a low thermal expansion coefficient. The support cylinder will provide valuable passive thermal isolation for the spacer, as well as a symmetric support structure and attenuation of stresses from mounting the device to the spacecraft.

This work is being supported on Grant NNG05GH33G from NASA under the Beyond Einstein Foundation Science Program. The goal is to evaluate cavity designs that could be adapted for use in the LISA gravitational wave mission and in other NASA missions, such as the GRACE Follow-On mission. Finite element calculations on the cavity design were generously provided by Till Rosenband of NIST. The cavity design is a modification of laboratory designs developed and tested by Mark Notcutt and John Hall of JILA and collaborators. Advice from Jim Berquist of NIST and from Bill Klipstein of JPL is also appreciated.

Discussion (8)

 


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