Objectives  There are obvious seasonal variations in the GPS height time series, which affect the improvement of precision and can be corrected by both mathematical modelling and geophysical mechanisms. Compared to least square fitting, singular spectrum analysis (SSA) can extract random seasonal signals effectively through signal reconstruction, which is unaffected by the assumed sinusoidal waves. According to the elastic loading theory, the gravity recovery and climate experiment (GRACE) can be used to calculate the vertical surface displacement caused by changes in terrestrial water storage.

  Methods  This paper mainly studies the feasibility of correcting the seasonal variations in GPS heights using SSA and GRACE inversion results. The height time series of 27 GPS stations in Australia with a time span of from 5 to 10 years were chosen and combined with GRACE simultaneous inversions.

  Results  Because the spatial resolutions of GRACE are coarse and the loading displacement is much more sensitive to near-field mass changes than far-field ones, the amplitudes of GRACE-inferred hydrological loading deformations are significantly smaller than GPS. The weighted root mean square (WRMS) are reduced at 22 stations after GRACE-inferred displacement corrections, and the correlation coefficients between deformations estimated by GPS and GRACE range from 0.12 to 0.78 with a mean value of 0.43, indicating that GPS and GRACE results have good consistency and correlation. SSA is used to extract the annual signals of vertical displacements derived from GPS and GRACE, and contribution rates of singular spectral variance of annual signals are 21.60% and 34.48%, respectively, expressing that annual signals are the main components of GRACE-inferred results. Geographical climatic conditions have a significant impact on the consistency of annual signals derived from GPS and GRACE. Compared with the arid areas in central and western Australia, the amplitude and phase of annual signals derived from GPS and GRACE are more consistent in the northern region with seasonal rainfall. Furthermore, cross wavelet transform (XWT) finds that the vertical displacement series derived from GPS and GRACE of each station have a significant resonance period of one year. The circular average phase angles of GPS/GRACE at the period closet to 1 cycle per year (cpy) outside the cone of influence range from -74.03° to 67.23°. The mean XWT-based semblances range from 0.28 to 0.99 with an average value of 0.79, showing that there is a significant positive correlation between the annual variations derived from GPS and GRACE.

  Conclusions  Overall, GRACE-inferred deformations can explain the annual variations of GPS-derived displacements, particularly in areas with high hydrological loading. It is possible to correct the annual signals of GPS heights by GRACE inversions, but the effect is not as good as the SSA-filtered annual signals.