Adaptive Sampling And Prediction Dynamical Systems Methods for Adaptive Sampling ASAP Kickoff Meeting June 28, 2004 Shawn C. Shadden (PI: Jerrold Marsden) California Institute of Technology

Methods for Studying Flow First method: integration of trajectories Kathrin Padberg

Methods for Studying Flow Second method: trajectories with high expansion rates

Methods for Studying Flow Third method: in-depth analysis of stretching (DLE) and transport barriers (LCS) LCS based on HF-radar data Drifter data collected from AOSNII Shadden, Lekien, Marsden (2004)

Information provided by Dynamical Systems theory Observables Upwelling source Barriers in the flow Regions with qualitatively different dynamics. DS Structures Regions of high DLE Ridges of the DLE field, i.e. LCS, LCS divide the domain in dynamical regions. LCS is a tool to help understand and visualize the global flow structure and dynamical patterns without having to compute and visualize each constituent trajectory.

Continue Developing Dynamical System Tools Explore and improve the use of 2-D LCS for Front Tracking /Prediction, and Lagrangian Predictions Study Characteristic modes of flow –Find time-scale of dynamically unique modes –Use to compute corresponding LCS Extend LCS to 3-D! Task 1:

LCS for sensor coverage Use LCS to partition flow into regions of different characteristic behavior –Determining sampling regions for gliders is simplified –Correlation between DLE and local statistics –Find best time/location for deployment and recovery Task 2:

LCS for Optimal Path Planning Use LCS to help reconfigure gliders during transit periods Optimal Path vs LCS: (Preliminary result) Task 3:

Interface Data What’s needed for success? DLELCS Near Optimal Paths Lagrangian Fronts Velocity Field Coastal Geometry Operate Vehicles Model Data OMA HF Radar Data Drifter Paths Glider Data Opportunity Asset Allocation