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Vertical land motion (VLM) of the Earth's crust occurs over diverse spatial and temporal scales, driven by surface mass-loading, anthropogenic influences, and tectonic processes (e.g., Pfeffer et al., 2017). VLM provides the key connection between relative sea-level (RSL) derived from a tide gauge (TG) and absolute sea-level (ASL) derived from a satellite altimeter (ALT, e.g., Church & White, 2011). ASL data is mainly comprised of ALT-inferred time series with a near-global coverage, while RSL is typically observed along well-developed coasts (Neumann et al., 2015). In the areas with sparse long-term TG records, improved understanding of VLM is critical to help plan better sea-level rise adaptation pathways at local and regional scales (Cazenave et al., 2014;Church et al., 2013;Woodworth et al., 2011).VLM at TG locations is obtained from geodetic observations or, in many cases, inferred from models of glacial isostatic adjustment (GIA). VLM is directly observable using space-borne techniques such as GNSS (of which global positioning system (GPS) is the most frequently used, for example, Hammond et al., 2016;Santamaría-Gómez et al., 2011), and TG VLMs are often interpolated from GPS velocities (e.g., Bouin & Wöppelmann, 2010). In the absence of nearby GPS, GIA rates are alternatively applied (e.g., Hay et al., 2015;Spada & Galassi, 2012), with an often-untested assumption that GIA is the dominant contributor to VLM.

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We further developed a space–time Kalman approach to investigate time-fixed and time-variable signals in vertical land motion (VLM) and residual altimeter systematic errors around the Australian coast, through combining multi-mission absolute sea-level (ASL), relative sea-level from tide gauges (TGs) and Global Positioning System (GPS) height time series. Our results confirmed coastal subsidence in broad agreement with GPS velocities and unexplained by glacial isostatic adjustment alone. VLM determined at individual TGs differs from spatially interpolated GPS velocities by up to ~ 1.5 mm/year, yielding a ~ 40% reduction in RMSE of geographic ASL variability at TGs around Australia. Our mission-specific altimeter error estimates are small but significant (typically within ~  ± 0.5–1.0 mm/year), with negligible effect on the average ASL rate. Our circum-Australia ASL rate is higher than previous results, suggesting an acceleration in the ~ 27-year time series. Analysis of the time-variability of altimeter errors confirmed stability for most missions except for Jason-2 with an anomaly reaching ~ 2.8 mm/year in the first ~ 3.5 years of operation, supported by analysis from the Bass Strait altimeter validation facility. Data predominantly from the reference missions and located well off narrow shelf regions was shown to bias results by as much as ~ 0.5 mm/year and highlights that residual oceanographic signals remain a fundamental limitation. Incorporating non-reference-mission measurements well on the shelf helped to mitigate this effect. Comparing stacked nonlinear VLM estimates and altimeter systematic errors with the El Niño-Southern Oscillation shows weak correlation and suggests our approach improves the ability to explore nonlinear localized signals and is suitable for other regional- and global-scale studies.

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