Open water systems are one of the most externally influenced systems due to their size and continuous exposure to uncertain meteorological forces. The control of systems under uncertainty is, in general, a challenging problem. In this paper, we use a stochastic programming approach to control a drainage system in which the weather forecast is modeled as a disturbance tree. Each branch of the tree corresponds to a possible disturbance realization and has a certain probability associated to it. A model predictive controller is used to optimize the expected value of the system variables taking into account the disturbance tree. This technique, tree-based model predictive control (TBMPC), is solved in a distributed fashion. In particular, we apply dual decomposition to get an optimization problem that can be solved by different agents in parallel. In addition, different possibilities are considered in order to reduce the communicational burden of the distributed algorithm without reducing the performance of the controller significantly. Finally, the performance of this technique is compared with others such as minmax or multiple MPC.