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Bayesian Nonlinear Assimilation of Eulerian and Lagrangian Coastal Flow Data
P.F.J. Lermusiaux, P.J. Haley, Jr.,
Deepak N. Subramani

Massachusetts Institute of Technology
Center for Ocean Engineering
Mechanical Engineering
Cambridge, Massachusetts

Project Summary
Ongoing MIT-MSEAS Research
Additional Bayesian DA Links
Background Information

 

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This research is sponsored by the Office of Naval Research

Project Summary

The long-term goal of this project is to develop and apply theory, schemes and computational systems for rigorous Bayesian nonlinear assimilation of Eulerian and Lagrangian coastal flow data, fully exploiting nonlinear governing equations and mutual information structures inherent to coastal ocean dynamical systems and optimally inferring multiscale coastal ocean fields for quantitative scientific studies and efficient naval operations. The motivation is to exploit the information provided by coastal platforms (drifters, floats, gliders, AUVs or HF-radars) so as to best augment the limited resolution and accuracy of satellite data in coastal regions and to determine coastal sampling needs for successful Bayesian field estimation in diverse coastal regimes. Our aim is not to shy away from the known nonlinearities and unstationary heterogeneous statistics, but to utilize these known information structures, for robust and accurate Bayesian estimation.

Background information is available below.

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Ongoing MIT-MSEAS Research

Long-Term Goal:

Develop and apply theory, schemes and computational systems for rigorous Bayesian nonlinear assimilation of Eulerian and Lagrangian coastal flow data, fully exploiting nonlinear governing equations and mutual information structures inherent to coastal ocean dynamical systems and optimally inferring multiscale coastal ocean fields for quantitative scientific studies and efficient naval operations.

Objectives:

Presentations and Meetings

Bayesian DA-supported Publications

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Additional Bayesian DA Links

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Background Information

The coastal ocean is a prime example of multiscale nonlinear fluid dynamics. This is a consequence of turbulence, surface waves, internal waves, tides, internal tides, eddies, jets and currents, inflows from rivers, coastal winds inducing upwelling of cold, nutrient-rich waters, and rings and eddies from the deeper ocean drifting onshore, together with various other remote influences. Ocean fields (e.g. velocity, temperature and salinity fields) in such coastal regions are complex and intermittent, with multiple scales and unstationary heterogeneous statistics. The accurate simulation of these complex fields and statistics is challenging. Due to the limited measurements, there are multiple sources of uncertainties, including the initial conditions, boundary conditions, forcing, parameters and even the model parameterizations and equations themselves. For optimal scientific studies and naval operations, data assimilation in these regions should combine the information contained in measurements with that predicted by models in accord with the known complexities of the probability density functions (pdfs). To do so, the notion of covariance functions should be replaced by information-theoretic concepts such as mutual information functions among state variables or other relevant attributes. Such rigorous estimation based on governing equations and information theory is one of the critical motivation for our effort. Our aim is not to shy away from the known nonlinearities and unstationary heterogeneous statistics, but to fully exploit these known information structures and correspondences, for robust and accurate Bayesian nonlinear estimation.

Another critical motivation stems from the limited resolution and accuracy of satellite Sea Surface Height (SSH) observations in coastal regions. Already in the open ocean, satellite data resolution is limited. This renders the assimilation of satellite data challenging. In coastal regions, the SSH data resolution is often not sufficient to resolve submesoscales and even mesoscales and the SSH data accuracy is limited in part due to the shallow depths and proximity to land. Hence, satellite SSH data needs to be augmented by velocity observations from other platforms such as drifters, floats, gliders, AUVs and HF-radars. Such local flow data can be interpreted as fixed-point position or velocity, i.e. Eulerian data, but also as fixed-parcel trajectory or velocity, i.e. Lagrangian data. Ideally, both information types, the Eulerian and the Lagrangian, should be utilized in the estimation. Our motivation is thus to fully exploit the information provided by coastal platforms and to determine the sampling needs for successful Bayesian field estimation in diverse coastal regimes. To do so, we plan to utilize, implement and further develop our differential-equation-based uncertainty prediction, the Dynamically Orthogonal (DO) equations (Sapsis and Lermusiaux, 2009, 2012; Ueckermann et al, 2013), and our Gaussian Mixture Model (GMM) nonlinear data assimilation schemes (Sondergaard and Lermusiaux 2013 a, b), the GMM-DO filters and smoothers. Our research focus is thus the Bayesian nonlinear assimilation of Eulerian and Lagrangian coastal flow data.

Our MSEAS structured finite-volume code for primitive-equation dynamics with a nonlinear-free-surface will be employed and further developed for the above research and regional ocean forecasting. This computational model is part of the MSEAS system which is employed in varied research projects (present efforts include AforSSIE, LEARNS, ACDTDA, IODA, ATL).

The publications cited in the above descriptions are available from: http://mseas.mit.edu/publications

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