A Functional Data Approach to the Argo Project

Drew Yarger, Tailen Hsing and Stilian Stoev, University of Michigan, Statistics, Ann Arbor, United States
We consider the problem of mapping and spatial prediction using the sparse profiles of Argo data from the perspective of functional data analysis (fda). In this framework, we estimate ocean properties at a fixed location and time as a continuous function of pressure. There are three motivations for our approach. First, we avoid the interpolation of profiles onto fixed pressure levels and estimate over the entire pressure dimension simultaneously. Second, fda provides a natural way to handle the dependence between measurements within the same profile. Lastly, natural properties of the functional estimates, including derivatives and integrals, can be leveraged for other scientific problems. The two main components of the technique are mean and covariance estimation. The mean approach combines two methods in nonparametric regression, smoothing splines and local regression, while the covariance estimation considers dependence across space, time and pressure. We demonstrate the mean and covariance estimation on the Argo temperature and salinity data and compare these with other mapping methods. There are considerable methodological and computational challenges due to the size of the data and the complex dependence between measurements within and between profiles. Our estimates are also implemented with interactive web applications using R Shiny.