Estimating vertical land motion and residual altimeter systematic errors using a Kalman-based approach

Vertical land motion (VLM) is the connection between absolute sea-level (ASL) from a satellite altimeter (ALT) and relative sea-level from a tide gauge (TG). VLM is often sparsely observed yet is required for understanding sea-level rise. Many studies have sought to exploit ALT and TG data to infer VLM, yet regionally correlated systematic errors in altimetry have not been considered. We have developed a Kalman filtering and smoothing framework to simultaneously estimate location-specific VLM and residual mission-specific systematic errors in a geocentric reference frame. We used ALT minus TG, ALT crossovers and global positioning system (GPS) bedrock height observations in a multi-stage solution approach that gradually separated time-variable parameter estimates in an ill-posed problem. We evaluated the performance of the method using the Jason-series along-track data in the Baltic Sea, where glacial isostatic adjustment is the dominant driver of VLM. We estimated local VLM variability at TGs of up to ∼4.5 mm/yr which is not evident in spatially interpolated GPS velocities. The estimated regional altimeter errors are significant and within the range of ∼±0.5–2.5 mm/yr. Our approach improves agreement between ASL estimates from ALT and TG records, provides a ∼20% decrease in root mean squared error of latitudinal ASL variability at TGs, and a reduction of the ASL rate from altimetry by ∼0.3 mm/yr across the region. This method advances the ALT-TG approach to determining VLM at TG locations and systematic errors of altimetry, which is broadly applicable to other regional- and global-scale studies.