Slow moving Autonomous Underwater Vehicles (AUVs) such as gliders typically run missions that take several days to weeks. When such vehicles are operating in coastal regions it is important to plan paths that avoid areas with high ship trafc. In previous work we proposed a minimumrisk method which can plan safe paths for gliders if the ocean currents are much slower than the speed of the glider. Unfortunately, ocean currents are usually strong enough to inuence the times of ight of gliders, such that they may experience very different routes and times of travel than those planned statically a priori. This results in vehicles surfacing in regions which may be high risk. In this paper, we propose a novel method of risk-averse planning which uses a predictive ocean model to plan a path that minimizes risk in the presence of ocean currents subject to constraints on the maximum time between consecutive surfacing locations and the total length of the path. We solve this problem by constructing a timeexpanded network and nding the minimum cost path from the source node to the goal node. Our algorithm nds a resource constrained path which exploits the ocean current eld while surfacing in low-risk areas. We discuss the results obtained in eld experiments in the Southern California Bight to evaluate our algorithm.