Objectives  The lack of water resources in North China has severely affected the further development of industry and agriculture in the region. Previous studies have shown that terrestrial water storage (TWS) in North China are in a long-term loss trend, but the inversion methods are different, and three-dimensional acceleration point-mass modeling approach (3D-PMA) provides a new way for inversion of changes in TWS.

  Methods  We invert TWS in North China from 2003 to 2014 based on 3D-PMA. 3D-PMA decomposes the changes of the satellite's perturbation force into the three directions of the coordinate axis, and establishes the least square equation through theoretical calculations and observations.We use the average spherical harmonic coefficients from 2003 to 2014 as the background model, and replace C₂₀ with satellite laser ranging (SLR) data. The monthly difference relative to the background model is used as the change in the spherical harmonic coefficient caused by the change in surface mass. For the ill-posed problems of least squares, the 600 km linear-type spatial constraint is adopted. In order to verify the results, spherical harmonic approach (SH) and the RL06 Mascon model released by Center for Space Research, University of Texas at Austin (CSR) are used for comparative analysis.

  Results and Conclusions  The inversion results of the 3D-PMA and SH approaches indicate that TWS in North China have been in a long-term loss trend, but the loss rates calculated by different methods have certain differences. The loss rate of 3D-PMA is -3.09$\mathrm{c}\mathrm{m}/\mathrm{a}$, and SH is -2.60$\mathrm{c}\mathrm{m}/\mathrm{a}$ while using RL06 data provided by CSR to inverse TWS in North China. According to the calculation results of the characteristic points, 3D-PMA and Mascon have a higher correlation, and the difference between SH and 3D-PMA is mainly due to the inconsistency of the striping noise constraint smoothing strategy.