Hayder salman department of mathematics unc chapel hill
Sponsored Links
This presentation is the property of its rightful owner.
1 / 6

Hayder Salman Department of Mathematics UNC-Chapel Hill PowerPoint PPT Presentation


  • 83 Views
  • Uploaded on
  • Presentation posted in: General

Towards Nonlinear Filtering in Lagrangian Data Assimilation. Hayder Salman Department of Mathematics UNC-Chapel Hill. Collaborators: Chris Jones, Kayo Ide. Sponsored by. The augmented approach for Lagrangian Data Assimilation (LaDA) :.

Download Presentation

Hayder Salman Department of Mathematics UNC-Chapel Hill

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Towards Nonlinear Filtering in Lagrangian Data Assimilation

Hayder Salman

Department of Mathematics

UNC-Chapel Hill

Collaborators: Chris Jones, Kayo Ide

Sponsored by


The augmented approach for Lagrangian Data Assimilation (LaDA):

  • Traditionally, velocity field reconstructed from drifter observations

    • reconstructed velocity field assimilated into the model

    • problematic since drifter positions and velocity related nonlinearly

    • nonlinear observation operator

  • Introducing the augmented state vector

    • results in a linear observation operator

    • drifter positions assimilated directly into the model


Kalman Filter:

  • At analysis we update the state vector with

  • This produces the correct (Bayesian) solution provided

    • observation operator is linear

    • likelihood is Gaussian

    • prior is Gaussian

  • Need to rethink last point

    - generally not true for nonlinear models


Nonlinear Attributes of Lagrangian Data:

  • Important observation

    • very simple simple Eulerian velocity fields can give rise to Lagrangian chaos

  • Augmented system is strongly nonlinear in observation space (i.e. with respect to Lagrangian drifter trajectories.

Lagrangian coherent structures in double gyre ocean model

Ottino ARFM (1990)


Filter Performance Near Saddle:

  • The nonlinearity associated with chaotic advection is problematic in LaDA

    • filter divergence observed near a Lagrangian saddle

  • Augmented system is strongly nonlinear with respect to the space of the drifters

    - we need a Lagrangian specific component for our LaDA filter


Nonlinear Filtering for LaDA:

  • A full solution to the nonlinear problem requires

    • computing the transitional PDF from the Fokker-Planck equation (*)

    • computing the posterior PDF from the prior and likelihood using Baye’s rule

  • We would like to identify a specific structure in (*) to improve the approximation

    of the PDF in observation space

  • Under certain assumptions, the PDF associated with the evolution of a drifter is

    related to an advection-diffusion equation of a passive tracer !!!

  • We are exploiting the simplification associated with this property to formulate a

    more general method for LaDA.


  • Login