**Statistical framework**

The resolution of the global sea level budget can broadly be defined as multivariate inversion in four dimensions combined with source separation. This is a problem not just relevant for geosciences, but for any discipline where spatial fields vary in time (e.g. biology, medical imaging, astronomy). We have multiple, irregularly distributed (in both time and space) observations with different spatial resolutions/footprints that are affected by a larger number of processes, which we want to solve for. This is, thus, an under-determined problem and requires prior information to enable the separation of the processes influencing the observations.

This is an active area of research in applied statistics [1] [2] but, here, we also have the added challenge of handling a spatially and temporally heterogeneous suite of observations exceeding 109 independent measurements, even after data pre-processing and spatio-temporal averaging. Thus, some form of dimensional reduction is essential to make the problem computationally tractable [3].

The Bayesian Hierarchical Model (BHM) to be utilised in the GlobalMass project makes use of several recent improvements in statistical modelling which are beneficial for geophysical applications. A detailed description of the mathematical methods to be employed are given in [3].

A key challenge in work package 1 – which underpins all other work packages – will be full parallelisation of the BHM, ensuring computational efficiency [4] and defining the meshes at a global scale for the five latent geophysical processes. For example, it will not be possible to determine the mass balance of an individual glacier. Rather, glaciated regions or sectors will be defined that are consistent with the observational resolution, which in itself, is not a constant (see, for example [5]). Developing the observation model requires an understanding of the data characteristics, the properties of the latent processes and how they influence the observations and forms a key task in WP1.

Next page: Progress

**References**

[1] Cressie, N. and A. Zammit-Mangion (2015) “Multivariate Spatial Covariance Models: A Conditional Approach.” ArXiv e-prints.

[2] Nychka, D., S. Bandyopadhyay, D. Hammerling, F. Lindgren and S. Sain (2014). “A multi-resolution Gaussian process model for the analysis of large spatial data sets.” J. Computational and Graphical Statistics 24(2): 579-599.

[3] Zammit-Mangion, A. B., Jonathan L.; Schoen, Nana W.; Rougier, Jonathan C. (2015). “A data-driven approach for assessing ice-sheet mass balance in space and time.” Annals of Glaciology 56(70): 175-189.

[4] Wikle, C. and N. Cressie (1999). “A dimension-reduced approach to space-time Kalman filtering.” Biometrika 86(4): 815-829.

[5] Jacob, T., J. Wahr, W. T. Pfeffer and S. Swenson (2012). “Recent contributions of glaciers and ice caps to sea level rise.” Nature 482(7386): 514-518.