This fellowship is concerned with building new statistical modelling and estimation procedures that are appropriate for Big Data challenges with high-dimensional dependent data. The new methods will be applied to large oceanographic spatiotemporal datasets leading to important application benefits in global climate modelling. The methodological contribution centres on building physically-motivated stochastic processes that capture multivariate dependence structure from complex high-dimensional data sets. Estimation procedures are then developed to capture heterogeneity in spatiotemporal data, while properly accounting for practical issues such as irregularly-sampled data in space and time. Such modelling and estimation procedures provide great interpretability and meaningful summaries from the complex data sets we observe. The societal benefits include improved global climate modelling and improved responses to environmental disasters such as oil spills.These advances will be achieved through interdisciplinary collaboration, with the fellow working closely with world-leading experts in oceanographic data in the US during the outgoing phase, and then consolidating these developments at the UCL Department of Statistical Sciences in the return phase. The fellow will therefore gain experience in developing relevant new statistical methods for a pressing Big Data challenge, and will then return to Europe where this training will significantly develop the fellow’s ability to produce cutting-edge research at the frontier of statistics and numerous applications involving complex high-dimensional data.