Constraining transient solid Earth rheology using satellite orbit perturbations to assess the dynamics of climate change

Monitoring essential climate variables such as Sea level rise, Earth’s Energy Imbalance, and ice-mass changes relies critically on space-geodetic observations of surface deformation and variations of the gravity field.
In particular, satellite geodesy provides decades-long, globally consistent records that are fundamental for quantifying climate-driven surface mass redistribution. However, these observations integrate both mass changes from the oceans, atmosphere, cryosphere and continental hydrology and the associated solid Earth response. Isolating climate variables from geodetic data therefore requires models that reflect the solid Earth response across timescales relevant to contemporary variability.
Yet, a critical assumption underlies much of current space-geodetic standard processing: the solid Earth response to surface mass variations is treated as purely elastic, i.e. instantaneous and fully recoverable. However, there is a growing body of evidence from laboratory rock mechanics experiments and geophysical observations suggesting that the Earth’s mantle exhibits a time-dependent, recoverable anelastic response across intermediate timescales  that could significantly affect geodetic at decadal to centennial timescales.
Here, we exploit several decades of Satellite Laser Ranging (SLR) observations towards passive spherical satellites to constrain key parameters governing the time-dependent mantle anelasticity. Owing to long-term measurements and sensitivity to low-degree gravity field variations, including solid Earth tides (C20, C30) and the pole tide (C21/S21), SLR observations are particularly well suited to probing deep Earth mantle rheology over decadal timescales.
We combine analytical orbit perturbation theory with the Hill-Clohessy-Wiltshire equations to quantify the sensitivity of the SLR observables to rheology and to choose an optimal parametrization. We then numerically estimate the solid Earth transient rheological properties from the SLR time series using an anelasticity framework consistent with seismic attenuation theory. Our results are compared with independent rheological constraints and yield a new set of frequency-dependent Love numbers that capture the Earth’s mantle transient rheology across decadal timescales.
We further show that accounting for this  transient rheology by incorporating the corresponding frequency-dependent Love numbers into the modeling of solid Earth tides, pole tide and surface loading-induced deformation, introduces systematic differences in climate-relevant geodetic time-series, including  satellite altimetry sea level rise estimates and ocean mass trends derived from satellite gravimetry.
More broadly, our results show that as space geodetic records become longer, data processing cannot rely solely on an  elastic solid Earth assumption. Instead, it must account for solid Earth transient rheology and the fact that geodetic observables will increasingly depend on the cumulative loading history, strengthening the need for interdisciplinary geodetic, geophysical and climate studies.