EOF-based constrained sensor placement and field reconstruction from noisy ocean measurements: Application to Nantucket Sound

Abstract

Sensor placement at the extrema of empirical orthogonal functions (EOFs) is efficient and leads to accurate reconstruction of the ocean state from a limited number of measurements. In this paper, we develop important new extensions of this approach that optimize sensor placement to avoid redundant measurements, employ imperfect EOF modes, and take into account measurement errors. We use the simulation outputs of the Finite Volume Community Ocean Model applied to the Nantucket Sound region to evaluate the performances of the new approach and compare it against other similar techniques. Specifically, we find that there exists a critical size of exclusion volume (whose value is unknown a priori) surrounding each sensor that prevents clustering of sensors while minimizing the reconstruction error. In addition, we propose a new algorithm that can be effective in incorporating gappy data in assimilation schemes. We also derive analytical formulas of the uncertainty in the reconstructed field given any inaccuracies in the measurements. Taken together these developments will aid further in the development of truly real-time adaptive sampling for ocean forecasting.