Sampling methods for improved benthic habitat maps based on reducing integrated Bernoulli variance

Oceanographic sampling to improve our knowledge about benthic habitats is common nowadays. Underwater vehicles are used to explore the seafloor to enable refined habitat maps, but considering the limited available resources during the sampling efforts, one must plan the deployments carefully. This question of effective sampling designs for underwater vehicles motivates our work. We aim to improve the sampling by using statistical models for the habitat features and to define a sampling criterion based on expected information gain. The criterion we use here is the expected integrated Bernoulli variance which we relate to the variance of presence-absence of corals in our example. Under modeling assumptions relying on a latent Gaussian model and logistic models for presence-absence data, we show partly closed form solutions for this criterion. This enables effective calculations of several possible designs, which is required in adaptive operations as is sometimes useful on for instance autonomous underwater vehicles. We illustrate the criterion in synthethic examples and in a retrospective analysis of ground truth dataset from the Trondheim fjord in Norway.