Revisiting Climate-Driven Low-Degree Spherical Harmonic Variations through the Improved Reconstruction of Hydrospheric and Cryospheric Mass Redistributions

Summary The degree-2 spherical harmonic coefficients of Earth’s time-variable gravity field are highly sensitive to large-scale mass redistribution within the hydrosphere and cryosphere. Under contemporary global warming, climate-driven mass changes in these reservoirs are a dominant source, yet their individual contributions remain incompletely quantified. Traditional estimates based on hydrospheric models, filtered GRACE spherical harmonic solutions, or GRACE mascon products are limited by incomplete cryospheric representation, spatial leakage, and regularization biases. Here, we apply the Fingerprint Approach that solves the sea-level equation on an elastic Earth to generate geoid fingerprints for four barystatic processes: terrestrial water storage, the Greenland Ice Sheet, the Antarctic Ice Sheet, and mountain glaciers. Using these fingerprints and unfiltered GRACE/GRACE-FO Stokes coefficients for 2003–2024, we reconstruct the individual degree-2 coefficients C20, C21, and S21, along with the associated time series of Earth’s dynamic oblateness (J2) and the mass terms of polar motion excitation (₁^{mass}, ₂^{mass}). We evaluate the reconstructed contributions against residual geodetic observations from satellite laser ranging and Earth orientation parameters, after removing atmospheric, oceanic, and glacial isostatic adjustment effects. The combined hydrospheric and cryospheric reconstructions reproduce both the secular trends and annual cycles of the residual observed J2, ₁^{mass}, and ₂^{mass} series. Terrestrial water storage dominates the seasonal variability of J2, ₁^{mass}, and ₂^{mass}, whereas accelerated ice-mass loss from Greenland and Antarctica controls the secular trend, with mountain-glacier mass loss also contributing to the long-term trend in J2. The resulting polar motion excitation drift closely matches the residual geodetic estimate in both magnitude and direction, indicating that contemporary climate-driven mass redistribution can largely account for recent changes in residual geodetic observations, and demonstrating the value of fingerprint-based reconstructions for monitoring climate impacts on the Earth system.