The barystatic contribution to multi-decadal sea-level change in the 19th century.

Understanding long-term trends in mass loss is vital for assessing the (in)stability of ice sheets and glaciers and their subsequent contribution to global mean sea level. Observational estimates of mass loss from the Greenland and Antarctic Ice Sheets are scarce before the satellite era (i.e., 1990s), and from glaciers before the 1950s. A variety of modelling techniques (process-driven and statistical) have been employed to synthesise and extend observational estimates, so that much of the 20th century sea-level budget is closed within uncertainty. Despite this work, uncertainty remains, particularly for contributions prior to ~1940 and the 19th century.  Sea-level fingerprinting exploits the fact that the geometry of land-based water masses (i.e., ice sheets, glaciers, hydrological storage) and any changes (via loss or gain) will generate a unique gravitational equipotential surface (fingerprint). We apply this technique in a Monte-Carlo-based linear inversion model to isolate the globally averaged barystatic contribution from Greenland, Antarctica and glaciers over pentadal periods since 1813. We use a selection of long-duration tide gauges and high-resolution proxy-based sea-level reconstructions, with model-based glacio-isostatic adjustment (GIA), stero-dynamic, and terrestrial water storage corrections.  Our initial findings confirm the validity of the approach when comparing barystatic contributions to observed estimates for the last 50 years. Whilst uncertainty is significant for the 19th century, the barystatic contribution deviates from zero in different pentads. We also conduct a sensitivity analysis to evaluate the idealised locations/corrections required to enhance confidence in the inversion procedure.