Localized Estimation of Tide Model Error and Mass Anomalies from GRACE/GRACE-FO Inter-Satellite Ranging

Abstract

Despite improvements from the GOT5.6 ocean tide model adopted for RL07 processing, tide model error remains a significant source of temporal aliasing in GRACE gravimetry. This effect is felt particularly in shallow shelves with complex bathymetry and a larger than normal presence of nonlinear tides, as well as in regions where hydrodynamic models are least constrained by observations. The cornerstone altimetry missions used to constrain modern tide models rely on an open surface and are inclined at around 66 degrees, limiting their coverage and leaving high latitudes constrained primarily by in-situ measurements, high-inclination altimetry and hydrodynamic models. SWOT extends coverage to 78 degrees latitude, but remains dependent on an open surface and its record since 2022 falls short of separating several closely spaced tidal constituents. GRACE and GRACE-FO have effectively global coverage, an extended time series history, and observe mass distribution rather than surface level, making them uniquely suitable for tidal estimation in high-latitude and ice-covered regions despite GRACE's relatively poor spatial resolution.We utilize a localized formulation following Han et al. (2008) to estimate residual mass anomalies and tides from GRACE inter-satellite range-rate residuals. Surface mass is parameterized as equivalent water height on a regional grid, gravitational acceleration is calculated by point-mass approximation and integrated along the nominal orbits, and mass anomaly and tidal signals are recovered relative to the CSR background gravity field and ocean tide model. Per-pass state deviation vectors are estimated to absorb out-of-region errors, long wavelength orbit signals, and accelerometer errors. The temporal basis is evaluated at each observation epoch, allowing for simultaneous estimation of sub-daily tidal harmonic signals alongside mean mass anomalies over arbitrary averaging intervals and reducing the leakage of non-tidal signals into the tidal residual estimates.The regional mass anomaly inversion of GRACE residuals is ill-posed and requires an extensive regularization scheme to produce meaningful results. Range-rate data constrain an along-track projection of the mass field, and arc state deviation parameters often compete with the mass anomaly parameters for the same long-wavelength signals. We discuss the conditioning of the problem, the regularization strategies that yielded a stable solution in the current model, and the sensitivity of the recovered field to regularization weights.Validation of the current model against CSR global solutions for monthly mean mass anomalies confirms the estimator geometry, regularization, and arc parameterization. We then present preliminary residual tide estimates in areas of interest, such as the Weddell Sea, assessed against available bottom pressure records, with proposed extensions to other regions and potential improvements to the localized mass anomaly estimation scheme.