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Global land ice, hydrology and ocean mass trends

Periodic Reporting for period 4 - GlobalMass (Global land ice, hydrology and ocean mass trends)

Okres sprawozdawczy: 2021-02-01 do 2022-11-30

Sea level rise is likely to be one of the most serious and tangible consequences of future climate change and is, consequently, a critical research challenge. Confidence in future projections will largely be dictated by our ability to correctly account for observed sea level changes from the recent past and the different factors that caused those changes.
Globally-averaged sea level change is quantified using the global sea level budget, a ‘balance-sheet’ approach that accounts for all the factors that contribute to sea level rise. Three main factors control changes in sea level: (i) changes in ocean mass (from ice sheets, glaciers and water storage on land); (ii) changes in ocean density (largely from thermal expansion of sea water); and (iii) changes in the elevation of the ocean floor (largely from glacial isostatic adjustment, GIA, the ongoing process by which the Earth’s crust is rebounding from the last glacial maximum ~20,000 years ago).

Since the early-1990s there has been a revolution in our ability to ‘observe’ and measure each of these components through a combination of satellite and in situ approaches. However, these new datasets have varying spatial and temporal characteristics which makes them complex to combine using conventional techniques.
This complexity, coupled with their increasing size and cross-disciplinary nature, means that the different components of sea level budget have generally been tackled separately. This has led to puzzling and at times contradictory results that do not necessarily respect fundamental principles of the coupled land-ice-ocean-solid Earth system or exploit the full capabilities of the new datasets.

The GlobalMass project, by contrast, sought to tackle all components simultaneously at a global scale. It did this by adopting a powerful novel approach to analysing large amounts of spatio-temporal data – a Bayesian Hierarchical Model (BHM) – which allows us to estimate the most likely combination of all the components of the sea level budget along with an indication of the uncertainty of the estimates. A key advantage of the BHM approach is that it provides a rigorous way of differentiating between observations based on their varied characteristics (or ‘smoothness’) in space and time. This allows us to separate the contribution of the different geophysical processes relevant to sea level change. Additional constraints provided by prior knowledge and fundamental physical principles (such as conservation of mass) can be added to the BHM to improve this separation further still.

Thus, the overall aim of the project was to develop and use a BHM to produce simultaneous, global, statistically-rigorous estimates of all components of the sea level budget for a common time period. These components comprise (i) solid Earth deformation due to glacial isostatic adjustment (GIA); (ii) land ice mass trends; (iii) land hydrology trends; and (iv) steric trends due primarily to thermal expansion of the oceans. Each of these processes is derived from a data-driven approach (rather than the result of numerical modelling) and combine a wide range of satellite and in-situ data. They will, for the first time, be consistent with each other and with physical constraints on the coupled system.

There were six specific objectives:
1: Develop the BHM methodology and software to undertake multivariate spatio-temporal modelling at a global scale.
2: Obtain a data-driven solution for global GIA, consistent with satellite and GPS observations.
3: Reconcile the sea level budget for 1981-2020.
4: Produce spatially-distributed land ice mass balance trends for 1992-2020, consistent with in-situ and satellite-based observations.
5: Re-evaluate twentieth century sea level rise from the tide gauge record using the BHM approach.
6: Investigate catchment-scale land hydrology trends for 2003-2020.
The GlobalMass project ran from August 2016 to November 2022. Much of our work during this time was focussed on developing and testing the Bayesian Hierarchical Model (BHM) – the statistical framework that is fundamental to the main project aim and objectives.

A series of computational experiments saw us incrementally add data and complexity with the main aim of testing that the statistical framework was working correctly. We successfully developed a working version of the BHM that ‘solves’ for the sea level budget at a global scale. However, we are not yet confident that the results are robust and are aware that several issues and bugs remain. In particular, mass is not conserved correctly in the current solution and has proved challenging due to the computational demands associated with inverting a large number of observations over multiple processes over the entire surface of the Earth. Imposing mass conservation requires simultaneous solutions for all processes.

Key results achieved during the project include:
• A first application of a BHM to ‘solve’ the sea level budget at a global scale.
• The creation of a global GPS dataset to provide a ‘clean’ signal of glacial isostatic adjustment (GIA)
• A new data-driven estimate of glacial isostatic adjustment (GIA).
• A new estimate of the land ice contribution to sea level rise since 1992.
• A new estimate of uncertainties in future ice sheet contribution to sea level rise.
• A comprehensive analysis of the water budget closure on a global scale.
• An analysis of global salt budget from 2005-2015
• The application of a BHM approach to investigate ice mass trends for Antarctica and, specifically, the Antarctic Peninsula.
• Development of a Python GUI (Pygoda; that enables fast and efficient visualisation and analysis of large sets of geolocated time series.

To disseminate project results, we established a dedicated website ( and Twitter feed (@globalmassteam) and used these to provide regular updates and news in addition to more established means of dissemination such as scientific conferences, journal articles and non-specialist media outlets. A listing of all GlobalMass outputs is also maintained on the project website ( and we additionally produced and uploaded plain language summaries of published papers ( The website received, on average, >100 visitors per month from December 2019 to November 2022.

Subsequently, we have created a GlobalMass Zenodo Community as an open and persistent record of research outputs that acknowledge GlobalMass funding and are available as open access ( which currently contains >90 records (34 publications; 33 presentations; 16 posters; 8 datasets). At the time of writing, publications that have acknowledged GlobalMass funding have been cited ~1,650 times (
‘Proof of Concept’ funding has been awarded through the 4-D Modeller project ( which will enable us to continue to improve and, we hope, finalise the global sea level budget solution, as well as developing a software tool to allow Bayesian statistical inference to be applied more widely to 4D problems.