The Bayesian Hierarchical Model (BHM) methodology has been applied to the generation of ensemble ocean surface vector winds in a sequence of increasingly sophisticated models. This history is briefly reviewed to establish the approach to BHM development in atmosphere-ocean contexts. Recently, ensemble surface winds and wind stresses are obtained from BHMs, given data stage inputs from satellites and weather-center analyses. Process model distributions are based on leading order terms from a Rayleigh Friction Equation balance and from formulae for bulk transfers at the air-sea interface. The forcing ensembles exploit precise observations and precise specifications of error to infer error in ocean forecasts based on two different kinds of data assimilation (DA) systems; i.e., a sequential DA system in the Mediterranean Sea and a variational DA system in the California Current System. Plans for developments in the next level of sophistication in atmosphere-ocean BHMs will introduce process model breakthroughs to be discussed in the talk that follows (Wikle et al.).