Multi-output Gaussian processes (MOGPs) have been widely used to model small geographic and oceanographic data sets, because of their ability to provide confidence estimates for predictions. Causal relationships in oceanographic data mean that certain variables are primarily influenced by a small number of others, but existing MOGPs learn correlations between outputs that are actually unrelated, leading to significantly reduced predictive accuracy. We introduce the AcyGP model, which composes latent GPs using a directed acyclic graph (DAG) structure that is learned from the data. The algorithm prevents spurious correlations by only introducing inter-output correlations when improvement in likelihood justifies the increase in structure complexity. Evaluation of the AcyGP model demonstrates state of the art predictive performance on real geographic and oceanographic data.