Filtering is a necessary step in the Gravity Recovery and Climate Experiment (GRACE) data processing, but leads to signal leakage and attenuation obviously, and adversely affects the quality of global and regional mass change estimates. We propose to use the Tikhonov regularization technique with the L-curve method to solve a correction equation which can reduce the leakage error caused by filter involved in GRACE data processing. We first demonstrate that the leakage error caused by the Gaussian filter can be well corrected by our regularization technique with simulation studies in Greenland and Antarctica. Furthermore, our regularization technique can restore the spatial distribution of original mass changes. For example, after applying the regularization method to GRAEC data (2003-2012), we find that GRACE mass changes tend to move from interior to coastal area in Greenland, which are consistent with recent other studies. After being corrected for glacial isostatic adjustment (GIA) effect, our results show that the ice mass loss rates were 274 ± 30 and 107 ± 34 Gt/yr in Greenland and Antarctica from 2003 to 2012, respectively. And a 10 ± 4 Gt/yr increase rate in Greenland interior is also detected.

Crustal vertical deformation (CVD) observed by continuous GPS height time-series can be explained largely by surface loading effects recovered from both Gravity Recover and Climate Experiment (GRACE) and General Circulation Models (GCMs) data. We first show that lower degree CVD spatial spectrum due to the Earth's elastic response to a uniform surface loading plays more important roles than that of high-degree case. We then demonstrate that GRACE data with 300–400 km spatial resolution have the ability to detect 99 per cent power of global and regional CVD in spatial spectrum domain using a global frequency–wavenumber spectrum method. We can just use either GRACE or GCMs 36 degree/order (d/o) spherical harmonic coefficients (SHCs) which correspond to 500 km spatial resolution to acquire more than 90 per cent variance of total CVD modeled by up to 180 d/o SHCs at 98 per cent global gridpoints. Globally, CVD modeled by GRACE loading can explain 72 per cent annual amplitude and 69 per cent variance of GPS observed height time-series, which is better than the GCMs results of 64 per cent for annual amplitude and 41 per cent for variance. Using a three cornered hat method, we also show that the noise level of monthly averaged CVD is about 3 mm for both GPS height time-series and GRACE loading result, while that of GCMs result is only 1.3 mm.

We developed a new boundary-included inversion model to improve the terrestrial water storage (TWS) inverted from regional GPS vertical deformation data. Through defining a new disc load empirical function (DLEF) and considering the mass change effect from the near but outside region, the result shows the TWS is more reasonable than the one inverted directly. Six simulation tests further confirmed the effectiveness of the boundary-included model. Finally, our new boundary-included model was used to derive the TWS in the Pacific Rim of the western United States based on the GPS-observed vertical deformation information. The inversion results show that our boundary-included inversion model can effectively improve the inversion results by 10–20% in terms of variance reduction in the boundary regions.