Model parameter estimation using coherent structure coloring

Lagrangian data assimilation is a complex problem in oceanic and atmospheric modelling. Tracking drifters in large-scale geophysical flows can involve uncertainty in drifter location, complex inertial effects and other factors which make comparing them to simulated Lagrangian trajectories from numerical models extremely challenging. Temporal and spatial discretisation, factors necessary in modelling large scale flows, also contribute to separation between real and simulated drifter trajectories. The chaotic advection inherent in these turbulent flows tends to separate even closely spaced tracer particles, making error metrics based solely on drifter displacements unsuitable for estimating model parameters. We propose to instead use error in the coherent structure colouring (CSC) field to assess model skill. The CSC field provides a spatial representation of the underlying coherent patterns in the flow, and we show that it is a more robust metric for assessing model accuracy. Through the use of two test cases, one considering spatial uncertainty in particle initialisation, and one examining the influence of stochastic error along a trajectory and temporal discretisation, we show that error in the coherent structure colouring field can be used to accurately determine single or multiple simultaneously unknown model parameters, whereas a conventional error metric based on error in drifter displacement fails. Because the CSC field enhances the difference in error between correct and incorrect model parameters, error minima in model parameter sweeps become more distinct. The effectiveness and robustness of this method for single and multi-parameter estimation in analytical flows suggest that Lagrangian data assimilation for real oceanic and atmospheric models would benefit from a similar approach.

[1]  J. Marsden,et al.  Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensional aperiodic flows , 2005 .

[2]  Ruoying He,et al.  Tracking the long-distance dispersal of marine organisms: sensitivity to ocean model resolution , 2013, Journal of The Royal Society Interface.

[3]  George Haller,et al.  Spectral-clustering approach to Lagrangian vortex detection. , 2015, Physical review. E.

[4]  Christopher K. Wikle,et al.  Atmospheric Modeling, Data Assimilation, and Predictability , 2005, Technometrics.

[5]  John O. Dabiri,et al.  Coherent structure colouring: identification of coherent structures from sparse data using graph theory , 2016, Journal of Fluid Mechanics.

[6]  Stephan T. Grilli,et al.  Modeling the 26 December 2004 Indian ocean tsunami : Case study of impact in Thailand - art. no. C07024 , 2007 .

[7]  K. Cheung,et al.  Modeling near‐field tsunami observations to improve finite‐fault slip models for the 11 March 2011 Tohoku earthquake , 2011 .

[8]  Andrew M. Stuart,et al.  A Bayesian approach to Lagrangian data assimilation , 2008 .

[9]  J. Thiffeault,et al.  Braids of entangled particle trajectories. , 2009, Chaos.

[10]  D. Iudicone,et al.  The effect of the Basset history force on particle clustering in homogeneous and isotropic turbulence , 2014, 1401.5309.

[11]  P. Herrmann,et al.  Annual Cycle of Poleward Heat Transport in the Ocean: Results from High-Resolution Modeling of the North and Equatorial Atlantic , 1994 .

[12]  F. J. Beron-Vera,et al.  On the Lagrangian Dynamics of Atmospheric Zonal Jets and the Permeability of the Stratospheric Polar Vortex , 2006 .

[13]  G. Haller Finding finite-time invariant manifolds in two-dimensional velocity fields. , 2000, Chaos.

[14]  P. Holmes,et al.  Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , 1983, Applied Mathematical Sciences.

[15]  Christopher Jones,et al.  A coherent structure approach for parameter estimation in Lagrangian Data Assimilation , 2017, 1706.04834.

[16]  Gary Froyland,et al.  A rough-and-ready cluster-based approach for extracting finite-time coherent sets from sparse and incomplete trajectory data. , 2015, Chaos.

[17]  Ashwanth Srinivasan,et al.  On the modeling of the 2010 Gulf of Mexico Oil Spill , 2011 .

[18]  John O Dabiri,et al.  Identification of individual coherent sets associated with flow trajectories using coherent structure coloring. , 2017, Chaos.