Resolving Trends in Antarctic Ice Sheet Mass Loss and Glacio-isostatic Adjustment Through Spatio-temporal Source-separation

There remains considerable inconsistency between different methods and approaches for determining ice mass trends for Antarctica from satellite observations. There are three approaches that can provide near global coverage for mass trends: altimetry, gravimetry and mass budget calculations. All three approaches suffer from a source separation problem where other geophysical processes limit the capability of the method to resolve the origin and magnitude of a mass change. A fourth approach, GPS vertical motion, provides localised estimates of mass change due to elastic uplift and an indirect estimate of GIA. Each approach has different source separation issues and different spatio-temporal error characteristics. In principle, it should be possible to combine the data and process covariances to minimize the uncertainty in the solution and to produce robust, posterior errors for the trends. In practice, this is a challenging problem in statistics because of the large number of degrees of freedom, the variable spatial and temporal sampling between the different observations and the fact that some processes remain under-sampled, such as firn compaction. Here, we present a novel solution to this problem using the latest methods in statistical modelling of spatio-temporal processes. We use Bayesian hierarchical modelling and employ stochastic partial differential equations to capture our physical understanding of the key processes that influence our observations. Due to the huge number of observations involved (> 10^8) methods are required to reduce the dimensionality of the problem and care is required in treatment of the observations as they are not independent. Here, we focus mainly on the results rather than the full suite of methods and we present time evolving fields of surface mass balance, ice dynamic-driven mass loss, and firn compaction for the period 2003-2009, derived from a combination of ICESat, ENVISAT, GRACE, InSAR, GPS and regional climate model output data. We also present a time-invariant GIA field and an elastic vertical motion field for the bedrock. All fields are solved for simultaneously alongside posterior errors that are consistent with the full suite of observations and priors. The framework we have developed can incorporate other data, such as shallow/deep ice core records of accumulation, coffee-can point measurements of mass balance, and snow radar data. The framework can also be applied to other ice masses and components of the climate system that suffer similar source separation issues: for example, solving the sea level budget.