🤖 AI Summary
This study addresses the incomplete depth coverage of temperature–salinity profiles collected by deep-diving marine mammals in the Indian Ocean sector of the Southern Ocean, which arises from behavioral differences among individuals. To overcome this limitation, the authors propose a multivariate functional principal component analysis method incorporating geographic covariates. By modeling the mean and covariance structure of complete bivariate profiles, they construct eigenfunction bases and integrate a measurement error model to estimate conditional functional principal scores, enabling high-fidelity reconstruction of truncated profiles across the full depth range. In simulations, the approach improves reconstruction accuracy by 30% for temperature and 33% for salinity in the 20–500 m layer when applied to profiles truncated at 250 m. The method successfully reconstructs approximately 90,000 profiles across a 3-million-square-kilometer region surrounding the French subantarctic islands, marking the first large-scale, accurate recovery of incomplete oceanographic profiles.
📝 Abstract
We present a statistical method to reconstruct the vertical thermohaline conditions in the Indian Sector of the Southern Ocean, where temperature and salinity profiles are partially sampled by female southern elephant seals. Datasets collected by biologgers provide unprecedented spatial and temporal coverage of ocean conditions. However, the maximum recorded depth varies with the animals' behaviour, offering only a partial view of the vertical environment. Using multivariate functional Principal Component Analysis (PCA), a parametric estimation of the covariance structure and mean function from a set of complete bivariate profiles allows the construction of an eigenfunction basis. By accounting for measurement error variance, partially sampled temperature and salinity profiles can be projected into the eigenspace of the complete profiles through conditional estimation of their functional principal coordinates and then reconstructed over the defined domain. For simulated snippet profiles truncated at depth $z_{\max} = 250$ m and reconstructed over $\mathcal{Z} = [20,500]$ m, reconstruction accuracy increases by 30 % for temperature and 33 % for salinity when incorporating geographical covariates. We then reconstruct ~90,000 incomplete profiles from the multivariate functional PCA of ~10,000 profiles reaching 500 m, covering approximately 3 million km$^2$ around the French subantarctic islands.