Transportation costs still play an important role in the economics of commodity markets. In this paper I present a theoretical framework aimed at describing spatial arbitrage under uncertainty; I analyze the effect of changing transport costs on different, yet related, variables: volume of trade, volatility of prices, and levels of spatial price differentials. As a tribute to Enke and Samuelson the model is referred to as the stochastic Enke-Samuelson model. It provides predictions for variables (such as price volatilities or correlations) which cannot be defined in the deterministic framework of the standard spatial price equilibrium model. The statistical tests display a convergent array of evidence in favor of the model.