Time-optimal paths are evaluated by VISIR (“discoVerIng Safe and effIcient Routes”), a graph-search ship routing model, with respect to the solution of the fundamental differential equations governing optimal paths in a dynamic wind-wave environment. The evaluation exercise makes use of identical setups: topological constraints, dynamic wave environmental conditions, and vessel-ocean parametrizations, while advection by external currents is not considered. The emphasis is on predicting the time-optimal ship headings and Speeds Through Water constrained by dynamic ocean wave fields. VISIR upgrades regarding angular resolution, time-interpolation, and static navigational safety constraints are introduced. The deviations of the graph-search results relative to the solution of the exact differential equations in both the path duration and length are assessed. They are found to be of the order of the discretization errors, with VISIR's solution converging to that of the differential equation for sufficient resolution.

We develop and illustrate an efficient but rigorous methodology that predicts the time-optimal paths of ocean vehicles in continuous dynamic flows. The goal is to best utilize or avoid currents, without limitation on these currents or on the number of vehicles. The methodology employs a new modified level set equation to evolve a front from the starting point of a vehicle until it reaches the desired goal location, combining flow advection with nominal vehicle motion. The optimal path of the vehicle is then obtained by solving a particle tracking equation backward in time. The computational cost of this method increases linearly with the number of vehicles and geometrically with spatial dimensions. The methodology is applicable to any continuous flow and in scenarios with multiple vehicles. Present illustrations consist of the crossing of a canonical uniform jet and its validation using a classic optimization solution, as well as swarm formation in more complex time varying 2D flow fields, including jets, eddies and forbidden regions.

Uncertainty prediction for ocean and climate predictions is essential for multiple applications today. Many-Task Computing can play a significant role in making such predictions feasible. In this manuscript, we focus on ocean uncertainty prediction using the Error Subspace Statistical Estimation (ESSE) approach. In ESSE, uncertainties are represented by an error subspace of variable size. To predict these uncertainties, we perturb an initial state based on the initial error subspace and integrate the corresponding ensemble of initial conditions forward in time, including stochastic forcing during each simulation. The dominant error covariance (generated via SVD of the ensemble) is used for data assimilation. The resulting ocean fields are used as inputs for predictions of underwater sound propagation. ESSE is a classic case of Many Task Computing: It uses dynamic heterogeneous workflows and ESSE ensembles are data intensive applications. We first study the execution characteristics of a distributed ESSE workflow on a medium size dedicated cluster, examine in more detail the I/O patterns exhibited and throughputs achieved by its components as well as the overall ensemble performance seen in practice. We then study the performance/usability challenges of employing Amazon EC2 and the Teragrid to augment our ESSE ensembles and provide better solutions faster.