Nonhydrostatic, multiscale processes are an important part of our understanding of ocean dynamics. However, resolving these dynamics with traditional computational techniques can often be prohibitively expensive. We apply the hybridizable discontinuous Galerkin (HDG) finite element methodology to perform computationally efficient, high-order, nonhydrostatic ocean modeling by solving the Navier-Stokes equations with the Boussinesq approximation. In this work, we introduce a distributed implementation of our HDG projection method algorithm. We provide numerical experiments to verify our methodology using the method of manufactured solutions and provide preliminary benchmarking for our distributed implementation that highlight the advantages of the HDG methodology in the context of distributed computing. Lastly, we present simulations in which we capture nonhydrostatic internal waves that form as a result of tidal interactions with ocean topography. First, we consider the case of tidally-driven oscillatory flow over an abrupt, shallow seamount, and next, the case of strongly-stratified, oscillatory flow over a tall seamount. We analyze and compare our simulations to other results in literature.

Error Subspace Statistical Estimation (ESSE), an uncertainty prediction and data assimilation methodology employed for real-time ocean forecasts, is based on a characterization and prediction of the largest uncertainties. This is carried out by evolving an error subspace of variable size. We use an ensemble of stochastic model simulations, initialized based on an estimate of the dominant initial uncertainties, to predict the error subspace of the model fields. The dominant error covariance (generated via an SVD of the ensemble-generated error covariance matrix) is used for data assimilation. The resulting ocean fields are provided as the input to acoustic modeling, allowing for the prediction and study of the spatiotemporal variations in acoustic propagation and their uncertainties. The ESSE procedure is a classic case of Many Task Computing: These codes are managed based on dynamic workflows for the: (i) perturbation of the initial mean state, (ii) subsequent ensemble of stochastic PE model runs, (iii) continuous generation of the covariance matrix, (iv) successive computations of the SVD of the ensemble spread until a convergence criterion is satisfied, and (v) data assimilation. Its ensemble nature makes it a many task data intensive application and its dynamic workflow gives it heterogeneity. Subsequent acoustics propagation modeling involves a very large ensemble of short-in-duration acoustics runs.