  The Argo data is a modern oceanography dataset that provides unprecedented
global coverage of temperature and salinity measurements in the upper 2,000
meters of depth of the ocean. We study the Argo data from the perspective of
functional data analysis (FDA). We develop spatio-temporal functional kriging
methodology for mean and covariance estimation to predict temperature and
salinity at a fixed location as a smooth function of depth. By combining tools
from FDA and spatial statistics, including smoothing splines, local regression,
and multivariate spatial modeling and prediction, our approach provides
advantages over current methodology that consider pointwise estimation at fixed
depths. Our approach naturally leverages the irregularly-sampled data in space,
time, and depth to fit a space-time functional model for temperature and
salinity. The developed framework provides new tools to address fundamental
scientific problems involving the entire upper water column of the oceans such
as the estimation of ocean heat content, stratification, and thermohaline
oscillation. For example, we show that our functional approach yields more
accurate ocean heat content estimates than ones based on discrete integral
approximations in pressure. Further, using the derivative function estimates,
we obtain a new product of a global map of the mixed layer depth, a key
component in the study of heat absorption and nutrient circulation in the
oceans. The derivative estimates also reveal evidence for density inversions in
areas distinguished by mixing of particularly different water masses.
