Time-optimal path planning in dynamic flows using level set equations: realistic applications

The level set methodology for time-optimal path planning is employed to predict collision-free and fastest-time trajectories for swarms of underwater vehicles deployed in the Philippine Archipelago region. To simulate the multiscale ocean flows in this complex region, a data-assimilative primitive-equation ocean modeling system is employed with telescoping domains that are interconnected by implicit two-way nesting. These data-driven multiresolution simulations provide a realistic flow environment, including variable large-scale currents, strong jets, eddies, wind-driven currents, and tides. The properties and capabilities of the rigorous level set methodology are illustrated and assessed quantitatively for several vehicle types and mission scenarios. Feasibility studies of all-to-all broadcast missions, leading to minimal time transmission between source and receiver locations, are performed using a large number of vehicles. The results with gliders and faster propelled vehicles are compared. Reachability studies, i.e., determining the boundaries of regions that can be reached by vehicles for exploratory missions, are then exemplified and analyzed. Finally, the methodology is used to determine the optimal strategies for fastest-time pick up of deployed gliders by means of underway surface vessels or stationary platforms. The results highlight the complex effects of multiscale flows on the optimal paths, the need to utilize the ocean environment for more efficient autonomous missions, and the benefits of including ocean forecasts in the planning of time-optimal paths.United States. Office of Naval Research (Grant N00014-09-1-0676 (Science of Autonomy - A-MISSION))United States. Office of Naval Research (Grant N00014-07-1-0473 (PhilEx))United States. Office of Naval Research (Grant N00014-12-1-0944 (ONR6.2))United States. Office of Naval Research (Grant N00014-13-1-0518 (Multi-DA)

Variational Data Assimilation via Sparse Regularization

This paper studies the role of sparse regularization in a properly chosen basis for variational data assimilation (VDA) problems. Specifically, it focuses on data assimilation of noisy and down-sampled observations while the state variable of interest exhibits sparsity in the real or transformed domain. We show that in the presence of sparsity, the $\ell_{1}$-norm regularization produces more accurate and stable solutions than the classic data assimilation methods. To motivate further developments of the proposed methodology, assimilation experiments are conducted in the wavelet and spectral domain using the linear advection-diffusion equation

Forecast verification of a 3D model of the Mediterranean Sea. Analysis of model results and observations using wavelets and Empirical Orthogonal Functions.

The quality assessment of the three-dimensional GHER (GeoHydrodynamics and Environmental Research) model of the Mediterranean Sea is presented in this work. The verification of the model results is done in a spatio-temporal approach. Traditional error measures (i.e. correlation, mean error, etc) are very useful to assess the quality of a model, but they do not take into account the high complexity of three-dimensional models. The verification process is thus done in three main parts: first, the model is compared to observations and climatology in a qualitative approach, in order to make a preliminar study about the model behaviour. Then, the error assessment is done, using traditional statistic measures. In order to take into account the complexity of the model and observations, the last step in the verification process consists in a spatio-temporal analysis using wavelets and empirical orthogonal functions. This last analysis will allow us to have an insight about the model quality in a more detailed way. This verification process has been applied to the GHER model. This model is implemented in a two-way nesting approach in the Mediterranean Sea, Liguro-Provençal basin and Ligurian Sea, where the highest resolution is reached. Assimilation of sea surface temperature and sea level anomaly is made during a nine-week experiment. Another test is carried out, to assess the quality of sea surface temperature from the SOFT predictor of the Ligurian Sea. The predicted sea surface temperature is assimilated in the model and the quality of the forecast is compared to the first assimilation experiment. The assimilation of the SOFT statistical predictors can be very useful to force models in a real forecast experiment, where no observations are available