Numerics in Computational Engineering (NiCE)

Multi-Scale Data Assimilation Methods

One example of synergistic research activities is the new data assimilation methods for regional modeling developed by the NICE group in collaboration with the MIT Sea Grant PIs Changshen Chen and Robert Beardsley. Regional ocean forecasting is essential for effective diverse sea operations, e.g. coastal zones monitoring, fisheries management, pollution control and naval operations and data assimilation is a key to accurate forecasting. There is a wide range of spatio-temporal scales in the ocean with energetic variability, which is mostly intermittent and not known a priori. Observations -- required to initialize dynamical forecast systems – are difficult and costly, and sampling a pre-determined region uniformly in time-space is inefficient as only a small subset of those observations would have a significant effect on the accuracy of the forecasts.

Adaptive sampling is an evolving method for the efficient sampling of the most energetic ocean phenomena in support of real-time nowcasting and forecasting. It has been used only recently in ocean forecasting demonstrations and has the potential of reducing the observational requirements by two orders of magnitude. However, adaptive sampling is still complicated and costly for routine observations. Moreover, truly real-time adaptive sampling of the ocean requires fast data assimilation methods and rigorous criteria to identify locations of best sensor placement.

In light of ocean complexities over a wide range of scales, extracting the proper hierarchy can be valuable in physical understanding but also in developing new ways of modeling and forecasting ocean processes. Proper Orthogonal Decomposition (POD) is one such approach, (also known as the method of Empirical Functions or EOF), and some oceanographers have used it to analyze their data or to develop reconstruction procedures for gappy data sets. The work at MIT Sea Grant aims to build on the recent progress in four-dimensional coastal ocean modeling and data assimilation, autonomous ocean observing systems and new computational methods for the efficient reduction of complex dynamical systems. The work is novel because it involves multi-scale data-driven and evolving POD modes, which allow reduction of coastal ocean flows to their energetically dominant structures and provide new tools for rapid multi-scale ocean predictions. The low-dimensional approach leads to very small amount of data communicated to AUVs, and this makes the new method particularly useful given the current limited bandwidth in underwater communications.

The multiscale ocean involves spatio-temporal processes from 1 mm and 1 sec to thousands of km and hundreds of years. Reference: T. Dickey, Journal of Marine Systems, vol. 40, p. 5, 2003.

Modeling of Nantucket Sound: The selection of optimum locations of sensors is based on the extrema of the EOF modes – a method developed by the NICE group. Squares denote maxima whereas circles denote mnima of the EOF modes; also, shown in color are iso-contours of the second EOF mode of the velocity field. Reference: Yang et al, Journal of Geophysical Research, 2010.


[1] B. Yildirim, C. Chryssostomidis and G.E. Karniadakis, "Efficient sensor placement for ocean measurements using low-dimensional concepts", Ocean Modelling, vol. 27, pp. 160-173, 2009.

[2]X. Yang, D. Venturi, C. Cheng, Chryssostomidis and G.E. Karniadakis, "EOF-based constrained sensor placement and field reconstruction from noisy ocean measurements: Application to Nantucket Sound", J. Geophysical Research, doi:10.1029, 2010.

This page was last modified: August 4, 2014 10:48 am

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George Karniadakis
Research Scientist, MIT
Professor of Applied Mathematics, Brown University

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