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Dynamical Systems Methods for Dynamical Systems Methods for Adaptive SamplingAdaptive Sampling

ASAP Kickoff MeetingASAP Kickoff MeetingJune 28, 2004June 28, 2004

Shawn C. ShaddenShawn C. Shadden(PI: Jerrold Marsden)(PI: Jerrold Marsden)

California Institute of TechnologyCalifornia Institute of Technology

Methods for Studying FlowMethods for Studying Flow• First method: integration of trajectories

Kathrin Padberg (padberg@math.uni-paderborn.de)

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

Methods for Studying FlowMethods 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 Information provided by Dynamical Systems theoryDynamical 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 Continue Developing Dynamical System ToolsSystem 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:Task 1:

LCS for sensor coverageLCS 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:Task 2:

LCS for Optimal Path PlanningLCS for Optimal Path Planning

• Use LCS to help reconfigure gliders during transit periods

• Optimal Path vs LCS:(Preliminary result)

Task 3:Task 3:

Interface

Data

What’s needed for success?What’s needed for success?

DLE LCS

Near Optimal Paths

Lagrangian Fronts

Velocity Field

Coastal Geometry

Operate Vehicles

Model Data

OMA

HF Radar Data

Drifter Paths

Glider Data

Opportunity

Asset Allocation