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 similar 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 similar to +/- 0.5-2.5 mm/yr. Our approach improves agreement between ASL estimates from ALT and TG records, provides a similar to 20% decrease in root mean squared error of latitudinal ASL variability at TGs, and a reduction of the ASL rate from altimetry by similar to 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.

Automated summary

This study explores the relationship between absolute sea-level measured by a satellite altimeter and relative sea-level measured by tide gauge, developing a Kalman filtering and smoothing framework to estimate VLM and systematic errors in a geocentric reference frame. Evaluation in the Baltic Sea showed improved agreement between ALT and TG records, leading to a reduction in sea-level rise rate.