An Improved GPS-Inferred Seasonal Terrestrial Water Storage Using Terrain-Corrected Vertical Crustal Displacements Constrained by GRACE

Yongxin Liu,Hok Sum Fok

doi:10.3390/rs11121433

Abstract

Based on a geophysical model for elastic loading, the application potential of Global Positioning System (GPS) vertical crustal displacements for inverting terrestrial water storage has been demonstrated using the Tikhonov regularization and the Helmert variance component estimation since 2014. However, the GPS-inferred terrestrial water storage has larger resulting amplitudes than those inferred from satellite gravimetry (i.e., Gravity Recovery and Climate Experiment (GRACE)) and those simulated from hydrological models (e.g., Global Land Data Assimilation System (GLDAS)). We speculate that the enlarged amplitudes should be partly due to irregularly distributed GPS stations and the neglect of the terrain effect. Within southwest China, covering part of southeastern Tibet as a study region, a novel GPS-inferred terrestrial water storage approach is proposed via terrain-corrected GPS and supplementary vertical crustal displacements inferred from GRACE, serving as "virtual GPS stations" for constraining the inversion. Compared to the Tikhonov regularization and Helmert variance component estimation, we employ Akaike’s Bayesian Information Criterion as an inverse method to prove the effectiveness of our solution. Our results indicate that the combined application of the terrain-corrected GPS vertical crustal displacements and supplementary GRACE spatial data constraints improves the inversion accuracy of the GPS-inferred terrestrial water storage from the Helmert variance component estimation, Tikhonov regularization, and Akaike’s Bayesian Information Criterion, by 55%, 33%, and 41%, respectively, when compared to that of the GLDAS-modeled terrestrial water storage. The solution inverted with Akaike’s Bayesian Information Criterion exhibits more stability regardless of the constraint conditions, when compared to those of other inferred solutions. The best Akaike’s Bayesian Information Criterion inverted solution agrees well with the GLDAS-modeled one, with a root-mean-square error (RMSE) of 3.75 cm, equivalent to a 15.6% relative error, when compared to 39.4% obtained in previous studies. The remaining discrepancy might be due to the difference between GPS and GRACE in sensing different surface water storage components, the remaining effect of the water storage changes in rivers and reservoirs, and the internal error in the geophysical model for elastic loading.

Highlights

Terrestrial water storage (TWS), being one of the indispensable hydrological components, consists of surface water storage, groundwater, soil moisture, snow, and ice [1]
After introducing spatial Gravity Recovery and Climate Experiment (GRACE) data constraint points for the joint inversion according to the above criteria, the spatial pattern of all global positioning system (GPS)-inferred TWS exhibits similarities with the GRACE-inferred and Global Land Data Assimilation System (GLDAS)-modeled TWS, showing a pattern of increasing TWS amplitudes from the northwest to the southeast, which is attributed to the regional water storage characteristics in the study region (Figure 6b,e,h)
The GPS-inferred TWS with spatial data constraints, as well as the terrain correction, further strengthens the consistency of the TWS spatial pattern (Figure 6c,f,i) when compared to the cases with the GRACE-inferred and GLDAS-modeled TWS (Figure 7), indicating that the introduction of virtual GPS stations along with the terrain consideration is critical for the inversion process

Summary

Introduction

Terrestrial water storage (TWS), being one of the indispensable hydrological components, consists of surface water storage (e.g., reservoir and lake), groundwater, soil moisture, snow, and ice [1]. A geophysical observation model was set up via the well-known Green’s function [14] for converting the seasonal GPS VCD into TWS (hereinafter denoted as GPS-inferred TWS) with the Laplacian smoothness constraint [5]. The conversion process from the seasonal GPS VCD to the GPS TWS is fundamentally an ill-posed inverse problem, because the number of station observations is far fewer than the number of gridded parameters to be determined. Recent advances in geophysical data inversion that determines the regularization parameter tend to be in favor of the ABIC method It has been applied in the finite fault slip distribution inversion [29], Remote Sens.

GPS VCD Data

GRACE and GLDAS TWS Data

GPS Data Preprocessing

TWS Inversion Model and Methodology from an Annual Variation of GPS VCD

Results and Discussion

Conclusions