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Title: Akaike's Bayesian information criterion for the joint inversion of terrestrial water storage using GPS vertical displacements, GRACE and GLDAS in Southwest China
Authors: Liu, YX
Fok, HS
Tenzer, R 
Chen, Q
Chen, XW
Keywords: Terrestrial water storage inversion
Akaike's Bayesian information criterion
Issue Date: 2019
Publisher: Molecular Diversity Preservation International (MDPI)
Source: Entropy, July 2019, v. 21, no. 7, 664, p. 1-21 How to cite?
Journal: Entropy 
Abstract: Global navigation satellite systems (GNSS) techniques, such as GPS, can be used to accurately record vertical crustal movements induced by seasonal terrestrial water storage (TWS) variations. Conversely, the TWS data could be inverted from GPS-observed vertical displacement based on the well-known elastic loading theory through the Tikhonov regularization (TR) or the Helmert variance component estimation (HVCE). To complement a potential non-uniform spatial distribution of GPS sites and to improve the quality of inversion procedure, herein we proposed in this study a novel approach for the TWS inversion by jointly supplementing GPS vertical crustal displacements with minimum usage of external TWS-derived displacements serving as pseudo GPS sites, such as from satellite gravimetry (e.g., Gravity Recovery and Climate Experiment, GRACE) or from hydrological models (e.g., Global Land Data Assimilation System, GLDAS), to constrain the inversion. In addition, Akaike's Bayesian Information Criterion (ABIC) was employed during the inversion, while comparing with TR and HVCE to demonstrate the feasibility of our approach. Despite the deterioration of the model fitness, our results revealed that the introduction of GRACE or GLDAS data as constraints during the joint inversion effectively reduced the uncertainty and bias by 42% and 41% on average, respectively, with significant improvements in the spatial boundary of our study area. In general, the ABIC with GRACE or GLDAS data constraints displayed an optimal performance in terms of model fitness and inversion performance, compared to those of other GPS-inferred TWS methodologies reported in published studies.
EISSN: 1099-4300
DOI: 10.3390/e21070664
Rights: © 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (
The following publication Liu, Y.; Fok, H.S.; Tenzer, R.; Chen, Q.; Chen, X. Akaike’s Bayesian Information Criterion for the Joint Inversion of Terrestrial Water Storage Using GPS Vertical Displacements, GRACE and GLDAS in Southwest China. Entropy 2019, 21, 664, 1-21 is available at
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