By means of Bayesian hierarchical modeling (BHM), we develop a model for aspects of vigorous air-sea interactions on a basin scale. The approach relies on both physical reasoning and statistical techniques for data processing and uncertainty management. The theory and current practice of BHM of air-sea interaction physics will be introduced and demonstrated in this paper. The demonstration is in the context of an observing system simulation experiment. An ocean truth simulation is driven by idealized surface winds in a testbed domain abstracted from the Labrador Sea. Artificial observations analogous to scatterometer and altimeter data are supplied to a BHM and comparisons made with the evolution of the truth simulation over a ten day experiment. Substantial attention is devoted to description of computational techniques.