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Hybrid ensemble/variational estimation/forecasting and adaptive observation of environmental contaminant plumes in the atmosphere and ocean


The related challenges of determining where an (airborne or waterborne) environmental contaminant plume is being released, how the plume is distributed now, and how it will evolve in the near future, are of broad interest.  Recent example plumes of specific interest, in both the ocean and the atmosphere, include the oil leak from Deepwater Horizon, the ash cloud from the Eyjafjallajökull volcano in Iceland, and the radioactive materials released by Fukushima; plumes in the battlefield setting, for both offensive and defensive maneuvers (covering the movements of friendly assets with smoke, or evading chemical weapons), are also of interest.


In such problems, as in hurricane forecasting, it is insufficient to simply observe the flow phenomena from space; rather, targeted in situ sampling (of both the contaminant itself, as well as the winds that drive its movement) is essential.


This project hybridizes two powerful weather forecasting strategies, ensemble (EnKF) and variational (4Dvar/MHE) methods, and applies them to two related subproblems: data assimilation and adaptive observation.

  • Ensemble methods, which compare and contrast multiple parallel simulations of a certain physical phenomenon, are essential to characterize the principle “directions” (in phase space) of uncertainty in the system, which then become the primary focus of subsequent Bayesian measurement updates in a Kalman-like setting.

  • Variational methods, which revisit and reinterpret past measurements in light of new data, are of significant value in nonlinear systems, whose trajectories can effectively bifurcate.

  • In our hybrid formulation of the data assimilation (i.e., state estimation) problem, an ensemble of state trajectories and their adjoints are marched forward and back over the recent past, in order to reconcile recent measurements with the numerical model of the flow system.

  • Our (mathematically rigorous, and practically effective) hybrid formulation of the adaptive observation problem is effectively its dual, and builds squarely on an ensemble representation characterizing the current state estimate and its uncertainty; this ensemble of state trajectories and their adjoints are marched forward and back over the near future in order to optimize feasible trajectories of the sensor vehicles, over the (receding) time horizon considered, in order to minimize a targeted measure of the forecast uncertainty (the trace of a covariance matrix).

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