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 ([email protected])
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
DS Structures
• Regions of high DLE
• Barriers in the flow
• Ridges of the DLE field,
i.e. LCS,
• LCS divide the domain in
dynamical regions.
• Regions with qualitatively
different dynamics.
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.
Task 1: 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 2: 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 3: LCS for Optimal Path Planning
• Use LCS to help reconfigure gliders during transit
periods
• Optimal Path vs LCS:
(Preliminary result)
What’s needed for success?
Data
Coastal Geometry
Lagrangian Fronts
Model Data
Velocity Field
DLE
LCS
Asset Allocation
Near Optimal Paths
Opportunity
HF Radar Data
OMA
Drifter Paths
Glider Data
Interface
Operate Vehicles