Considering the unstable inversion of ill‐conditioned intermediate matrix required in each integral arc in the short‐arc approach presented in Chen et al. (2015, https://doi.org/10.1002/2014JB011470), an optimized short‐arc method via stabilizing the inversion is proposed. To account for frequency‐dependent noise in observations, a noise whitening technique is implemented in the optimized short‐arc approach. Our study shows that the optimized short‐arc method is able to stabilize the inversion and eventually prolong the arc length to 6 hr. In addition, the noise whitening method is able to mitigate the impacts of low‐frequency noise in observations. Using the optimized short‐arc approach, a refined time series of Gravity Recovery and Climate Experiment (GRACE) monthly models called Tongji‐Grace2018 has been developed. The analyses allow us to derive the following conclusions: (a) During the analyses over the river basins (i.e., Amazon, Mississippi, Irrawaddy, and Taz) and Greenland, the correlation coefficients of mass changes between Tongji‐Grace2018 and others (i.e., CSR RL06, GFZ RL06, and JPL RL06 Mascon) are all over 92% and the corresponding amplitudes are comparable; (b) the signals of Tongji‐Grace2018 agree well with those of CSR RL06, GFZ RL06, ITSG‐Grace2018, and JPL RL06 Mascon, while Tongji‐Grace2018 and ITSG‐Grace2018 are less noisy than CSR RL06 and GFZ RL06; (c) clearer global mass change trend and less striping noise over oceans can be observed in Tongji‐Grace2018 even only using decorrelation filtering; and (d) for the tests over Sahara, over 36% and 19% of noise reductions are achieved by Tongji‐Grace2018 relative to CSR RL06 in the cases of using decorrelation filtering and combined filtering, respectively.

Mass transport estimates based on filtered Gravity Recovery and Climate Experiment (GRACE) monthly spherical harmonic gravity field solutions generally suffer from resolution loss and signal attenuation. To develop high‐resolution solutions from GRACE Level‐1B data, this study proposes a new regularization method. Transforming spatial constraints from GRACE‐based filtered mass changes into the spectral domain and imposing them on spherical harmonics, we resolve high‐resolution gravity field solutions expressed as spherical harmonics instead of mascons. The proposed method greatly enhances the spatial resolution and signal strength of spherical harmonic solutions. Using the presented method, we have produced a time series of high‐resolution (degree 180) spherical harmonic solutions named Tongji‐RegGrace2019, which can be directly used without further smoothing. To evaluate Tongji‐RegGrace2019, we conduct the global (trend and annual amplitude) and regional comparisons (groundwater loss signals over India, hydrology signals over river basins, and ice melting signals over Greenland, Antarctica Peninsula and Patagonia) among various GRACE solutions. Our analyses show that Tongji‐RegGrace2019 agrees well with Center for Space Research and Jet Propulsion Laboratory mascon solutions in terms of signal power and spatial resolution. Over the selected areas, the correlation coefficients of mass changes between Tongji‐RegGrace2019 and mascon solutions are at least 82%. Compared to the filtered solution, higher spatial resolution and stronger signal power are achieved by Tongji‐RegGrace2019 and mascon solutions, which have the potential to retrieve signals at a smaller spatial scale. Over Patagonia Icefield, the improvement of trend estimates by Tongji‐RegGrace2019 with respect to the filtered solution is about 150%.

In this study, a new time series of Gravity Recovery and Climate Experiment (GRACE) monthly solutions, complete to degree and order 60 spanning from January 2003 to August 2011, has been derived based on a modified short‐arc approach. Our models entitled Tongji‐GRACE01 are available on the website of International Centre for Global Earth Models (http://icgem.gfz-potsdam.de/ICGEM/). The traditional short‐arc approach, with no more than 1 h arcs, requires the gradient corrections of satellite orbits in order to reduce the impact of orbit errors on the final solution. Here the modified short‐arc approach has been proposed, which has three major differences compared to the traditional one: (1) All the corrections of orbits and range rate measurements are solved together with the geopotential coefficients and the accelerometer biases using a weighted least squares adjustment; (2) the boundary position parameters are not required; and (3) the arc length can be extended to 2 h. The comparisons of geoid degree powers and the mass change signals in the Amazon basin, the Antarctic, and Antarctic Peninsula demonstrate that our model is comparable with the other existing models, i.e., the Centre for Space Research RL05, Jet Propulsion Laboratory RL05, and GeoForschungsZentrum RL05a models. The correlation coefficients of the mass change time series between our model and the other models are better than 0.9 in the Antarctic and Antarctic Peninsula. The mass change rates in the Antarctic and Antarctic Peninsula derived from our model are −92.7 ± 38.0 Gt/yr and −23.9 ± 12.4 Gt/yr, respectively, which are very close to those from other three models and with similar spatial patterns of signals.

The ill-posed models are widely encountered in various inversions of geodesy and remote sensing. The regularization approaches can significantly stabilize the solution to ill-posed models since the high-frequency noise is effectively suppressed. Although the famous Tikhonov regularization and truncated singular value decomposition (TSVD) regularization have been widely applied in various geodetic applications, there still remain theoretical drawbacks for either single regularization. For Tikhonov regularization, given a regularization parameter, the low-frequency terms are over-regularized, and high-frequency terms are under-regularized. For TSVD regularization, some medium-frequency terms will be mistaken for high-frequency terms to be truncated and the hidden signals will be lost. For this reason, we propose an adaptive regularized solution in spectral form, which adaptively divides the terms of different frequencies into three kinds: 1) the low-frequency terms are not regularized; 2) the medium-frequency terms are regularized by the Tikhonov method; and 3) the high-frequency terms are regularized by the TSVD method. The analytical conditions for determining the term sets are derived based on the criteria that the introduced biases should be smaller than the reduced errors; in other words, the mean square error (MSE) should be reduced. The two examples are presented to demonstrate the performance of our adaptive regularization. The first numerical example is solving the Fredholm integral equation of the first kind, which is widely encountered in remote sensing inversions. The simulations clearly demonstrate that the adaptive regularized solution can improve the MSE of ordinary Tikhonov and TSVD regularized functions by 25.00% and 9.09%, respectively. In the second example, we apply the new method to investigate the mass variation of the Yangtze River Basin based on the Gravity Recovery and Climate Experiment (GRACE) time-variable gravity field model. The Tongji-Grace 2018 monthly gravity field solutions from April 2002 to December 2016 are used to construct the mascon observation equation. The results show that our method also outperforms the ordinary Tikhonov and TSVD regularized solutions, with mean MSE reductions of about 13.40% and 11.69%, respectively. Furthermore, the spatial resolution of secular trend derived by our method is improved and the signal-to-noise ratio (SNR) of mass variation series is higher than the other two regularizations.