Akaike’s Bayesian Information Criterion for the Joint Inversion of Terrestrial Water Storage Using GPS Vertical Displacements, GRACE and GLDAS in Southwest China

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.

From the Great Recession to the COVID-19 Pandemic: The Risk of Expansionary Monetary Policies

“…It is a measure of model quality, which penalises complex models to prevent overfitting. In this definition, k is the number of estimated parameters, including initial states, and SSE is the sum of squared errors (Lopez and Weber 2017;Liu et al 2019). It is defined by Equation (5):…”

Analysis and Prediction of Terrestrial Water Storage Anomalies in the Lower Yangtze River Basin Based on an Improved Grey-Markov Model

“…The model drives four land-surface process models (i.e. Mosaic, Noah, 2002-4 to 2021-4 1979-1 to 2021-4 Missing Data 20022002-07;2003-06;2011-01;2011-06;2012-05;2012-10;2013-03;2013-08;2013-09;2014-02;2014-07;2014-12;2015-06;2015-10;2015-11;2016-04;2016-09;2016-10;2017-02;2017-07;2017-08;2017-09;2017-10;2017-11;2017-12;2018-01;2018-02;2018-03;2018-04;2018-05; The applicability of the GLDAS data in China has been proven by many researchers over the past few years (Hu et al, 2021;Li et al, 2021;Liu et al, 2019b;Qi et al, 2020). The results show that the Noah model data are of good quality in wet areas of China.…”

Upstream GPS Vertical Displacement and its Standardization for Mekong River Basin Surface Runoff Reconstruction and Estimation

“…GRACE-inferred terrestrial water storage (hereinafter called GRACE-S) also allows the calculation of solid Earth vertical surface deformation (e.g., [38][39][40][41]) that is consistent with the recorded global positioning system (GPS) vertical displacement (VD) (hereinafter called GPS-VD) (e.g., [42][43][44]), as demonstrated and validated in different geographic regions [45][46][47]. Conversely, the GPS-VD can also be utilized to infer the terrestrial water storage (e.g., [48][49][50][51]). Given the foregoing GRACE-inferred physical quantity that is comparable to the GPS-VD, it is anticipated that the latter can be a potential alternative for reconstructing the RWD; no paper in this regard has ever been published in recent literature.Essentially, the GRACE-S and its standardization have been recently demonstrated to have a good correlation with water level [52] and R [53].…”