Slow moving Autonomous Underwater Vehicles (AUVs) such as gliders typically run mis- sions 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 traffic. In previous work we proposed a minimum risk 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 influence the times of flight 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 predic- tive 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 finding the minimum cost path from the source node to the goal node. Our algorithm finds a resource constrained path which exploits the ocean current field while surfacing in low-risk areas. We discuss the results obtained in field experiments in the Southern California Bight to evaluate our algorithm.