A method for quantifying correlation in the shape of oceanographic profile data

Vertical profiles are a common type of oceanographic observation, involving measurements of a variable across a range of depths, and are widely used to identify physical and biogeochemical features of the water column. Recent studies have shown that oceanographic profiles can be represented as functional data objects, where each profile is treated as a single datum and expressed as a function of pressure. This study applies a recently developed technique, which defines a scalar correlation coefficient for functional data, to the analysis of oceanographic profiles. The method represents each profile using basis functions, whose associated weightings are termed basis coefficients, and quantifies dependence through the variability of these coefficients. An important advantage of this method is that the resulting correlation coefficient reflects similarities in overall profile shape, not just correlations between values at specific depths. Two applications of this method are explored: calculating the correlation coefficient between two different oceanographic variables, and estimating the temporal autocorrelation function of a single variable. Each application is demonstrated using two case study datasets: (1) the Coastal Endurance Washington Offshore Profiler Mooring and (2) biogeochemical-Argo floats. The first case study demonstrates how the method can be used to identify physical drivers of variability in biogeochemical profile structure. The second case study reveals regional differences in relationships between profiled variables and their temporal autocorrelation characteristics. This technique has broad potential for application to data from moorings, autonomous platforms, and ocean models, with possible use in observing system optimisation, data assimilation, and the analysis of vertically structured ocean processes.