Long-period hydrological polar motion excitation based on C21 and S21 coefficients from hybrid SLR+DORIS gravity solutions

Variations in Earth’s rotation result from a range of geophysical processes, including gravitational forcing by celestial bodies and mass redistribution within the atmosphere, oceans, hydrosphere, and cryosphere. The contributions of these processes to variability in the planet’s rotational motion are commonly quantified using four components of effective angular momentum: atmospheric (AAM), oceanic (OAM), hydrological (HAM), and cryospheric (CAM).

Hydrological angular momentum (HAM) describes the excitation of polar motion (PM) and length-of-day (LOD) variations caused by mass redistribution within the continental hydrosphere and can be estimated from global hydrological models, satellite-derived gravity field solutions, or climate model outputs. In this study, we reassess the mass-related excitation of PM by deriving the equatorial components (χ₁ and χ₂) of HAM from temporal variations in the C₂₁ and S₂₁ geopotential coefficients obtained from a new class of hybrid gravity field solutions. These solutions replace the conventional spherical harmonic representation with empirical orthogonal functions (EOFs) derived from Gravity Recovery and Climate Experiment (GRACE) data and fitted to Satellite Laser Ranging (SLR) and Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS) observations, enabling the construction of an extended time series spanning from 1984 to the present.

The resulting HAM time series are compared with estimates from global hydrological models and validated against the hydrological signal in geodetic angular momentum (GAO). The consistency between HAM and GAO is evaluated across multiple frequency bands, with particular emphasis on variability at periods longer than three years. In this low-frequency range, correlations between HAM derived from the hybrid solutions and GAO reach values of up to 0.9, indicating that hydrological signals inferred from temporal variations of the Earth’s gravity field account for a substantial fraction of the observed long-term PM excitation..

Typically, the agreement between GAO and HAM time series is analysed by comparing the χ₁ and χ₂ components separately. Here, we perform the analysis along the direction of maximum correlation, providing a more robust and physically meaningful assessment of the agreement between HAM and GAO.

These findings highlight  the importance of gravimetry-based HAM for interpreting PM variability across multiple time scales and extend earlier GRACE- and model-based investigations of hydrological PM excitation. In addition, this study provides the first long-term HAM estimates derived from hybrid SLR+DORIS gravity solutions spanning the period from 1984 to the present.