Processes in ocean physics, air–sea interaction and ocean biogeochemistry span enormous ranges in spatial and temporal scales, that is, from molecular to planetary and from seconds to millennia. Identifying and implementing sustainable human practices depend critically on our understandings of key aspects of ocean physics and ecology within these scale ranges. The set of all ocean data is distorted such that three- and four-dimensional (i.e., time-dependent) in situ data are very sparse, while observations of surface and upper ocean properties from space-borne platforms have become abundant in the past few decades. Precisions in observations of all types vary as well. In the face of these challenges, the interface between Statistics and Oceanography has proven to be a fruitful area for research and the development of useful models. With the recognition of the key importance of identifying, quantifying and managing uncertainty in data and models of ocean processes, a hierarchical perspective has become increasingly productive. As examples, we review a heterogeneous mix of studies from our own work demonstrating Bayesian hierarchical model applications in ocean physics, air–sea interaction, ocean forecasting and ocean ecosystem models. This review is by no means exhaustive and we have endeavored to identify hierarchical modeling work reported by others across the broad range of ocean-related topics reported in the statistical literature. We conclude by noting relevant ocean-statistics problems on the immediate research horizon, and some technical challenges they pose, for example, in terms of nonlinearity, dimensionality and computing.
"Modern Statistical Methods in Oceanography: A Hierarchical Perspective." Statist. Sci. 28 (4) 466 - 486, November 2013. https://doi.org/10.1214/13-STS436