  Improving and optimizing oceanographic sampling is a crucial task for marine
science and maritime resource management. Faced with limited resources in
understanding processes in the water-column, the combination of statistics and
autonomous systems provide new opportunities for experimental design. In this
work we develop efficient spatial sampling methods for characterizing regions
defined by simultaneous exceedances above prescribed thresholds of several
responses, with an application focus on mapping coastal ocean phenomena based
on temperature and salinity measurements. Specifically, we define a design
criterion based on uncertainty in the excursions of vector-valued Gaussian
random fields, and derive tractable expressions for the expected integrated
Bernoulli variance reduction in such a framework. We demonstrate how this
criterion can be used to prioritize sampling efforts at locations that are
ambiguous, making exploration more effective. We use simulations to study and
compare properties of the considered approaches, followed by results from field
deployments with an autonomous underwater vehicle as part of a study mapping
the boundary of a river plume. The results demonstrate the potential of
combining statistical methods and robotic platforms to effectively inform and
execute data-driven environmental sampling.
