The Gravity Recovery and Climate Experiment (GRACE) is a joint
National Aeronautics and Space Administration / Deutsches Zentrum für Luftund
Raumfahrt (NASA/DLR) mission to map the time-variable and mean
gravity field of the Earth, and was launched on March 17, 2002. The nature
of the gravity field inverse problem amplifies the noise in the data that creeps
into the mid and high degree and order harmonic coefficients of the earth's
gravity fields for monthly variability, making the GRACE estimation problem
ill-posed. These errors, due to the use of imperfect models and data noise, are
manifested as peculiar errors in the gravity estimates as north-south striping
in the monthly global maps of equivalent water heights.
In order to reduce these errors, this study develops a methodology
based on Tikhonov regularization technique using the L-curve method in combination
with orthogonal transformation method. L-curve is a popular aid for determining a suitable value of the regularization parameter when solving
linear discrete ill-posed problems using Tikhonov regularization. However, the
computational effort required to determine the L-curve can be prohibitive for
a large scale problem like GRACE. This study implements a parameter-choice
method, using Lanczos bidiagonalization that is a computationally inexpensive
approximation to L-curve called L-ribbon. This method projects a large
estimation problem on a problem of size of about two orders of magnitude
smaller. Using the knowledge of the characteristics of the systematic errors in
the GRACE solutions, this study designs a new regularization matrix that reduces
the systematic errors without attenuating the signal. The regularization
matrix provides a constraint on the geopotential coefficients as a function of its
degree and order. The regularization algorithms are implemented in a parallel
computing environment for this study. A five year time-series of the candidate
regularized solutions show markedly reduced systematic errors without any
reduction in the variability signal compared to the unconstrained solutions.
The variability signals in the regularized series show good agreement with the
hydrological models in the small and medium sized river basins and also show
non-seasonal signals in the oceans without the need for post-processing. / text
| Identifer | oai:union.ndltd.org:UTEXAS/oai:repositories.lib.utexas.edu:2152/7665 |
| Date | 02 June 2010 |
| Creators | Save, Himanshu Vijay |
| Source Sets | University of Texas |
| Language | English |
| Detected Language | English |
| Format | electronic |
| Rights | Copyright is held by the author. Presentation of this material on the Libraries' web site by University Libraries, The University of Texas at Austin was made possible under a limited license grant from the author who has retained all copyrights in the works. |
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