2. Understanding Atmospheric & Oceanic Flows: Laboratory Application of Cross-Correlation
David M. Holland
Courant Institute of Mathematical Sciences
New York University
June 10th, 2003
Faculty Resource Network Seminar

3. Seminar Schedule 09:00 – 10:00 Lecture – Cross Correlation
10:00 – 10:30 Laboratory Visit
(Room 103, 251 Mercer St. WWH)
10:30 – 11:30 MATLAB Computing Exercises
11:30 – 12: Group Presentations
(Answers to MATLAB Exercises)

4. Introduction to Lecture
Atmospheric & Oceanic Flows
Planetary Scale Flows – Feature Tracking
Laboratory Scale Flows – Particle Image Velocimetry
Cross Correlation Analysis
MATLAB Implementation – Particle Image Velocimetry

5. Atmospheric Flows
Jet Stream (Discovery Video)
Hurricane
Tornado

6. Oceanic Flows Great Conveyor Belt Gulf Stream
Further Information: Read Chapter 1 of Handout: The Oceans and Climate by Bigg

7. Planetary Scale Flows – Feature Tracking
Image “a”
Image “b”
Here are two sequential images (a and b) of chlorophyll-a data collected over the US east coast on May 8, 2000 by two different satellites at time spacing of 67 minutes.

8. Planetary Scale Flows – Feature Tracking
Flow Field Vectors - Derived by Feature Tracking Algorithm
Question: How are these flow arrows derived?

9. Laboratory Scale Flows – Particle Image Velocimetry (PIV)
Laboratory Analog of Planetary Scale Flows (Jet Stream)
PIV Principles
Further Information: Read Chapter 3 of Handout: Particle Image Velocimetry by Raffel et al.
NYU Laboratory

10. Cross Correlation Analysis – Basic Concepts
One-Dimensional Example
(Convolution, but similar to Cross Correlation)
Also use notation ‘*’ to indicate convolution

11. Cross Correlation Analysis – Image Displacement
Demonstration of Cross Correlation to find (dis)placement of one image within another (see MATLAB handout for details)
MATLAB
“demos”
Toolbox “Image Processing”
“Image Registration”
Set Path to “.”
Enter Commands

12. Cross Correlation Analysis – Fast Fourier Transform
One-Dimensional Example

13. Cross Correlation Analysis – Convolution Theorem
One-Dimensional Example
(using functions f(k) and g(k))
Convolution Theorem gives Convolution as Inverse Transform of Product of Fourier Transforms
where F and G represent Fourier Transform of f and g.

14. MATLAB Implementation – Particle Image Velocimetry (PIV)

15. Concluding Remarks – Cross Correlation
Atmospheric & Oceanic Flows are Complex – Laboratory Models Provide Insight
Particle Imaging Velocimetry –
Non-Invasive Measurement
Cross Correlation Analysis – Plays Central Role
Future Research – Faster/Better Computer Algorithms

16. Concluding Remarks – Educational Applications
MATLAB is a powerful teaching tool
Various Demo Modules for most all aspects of Mathematics
Interesting Applications of Statistics and Probability in the Geosciences
(e.g., Fluid Flow Measurement)
This Seminar Web Site available
(see Handout)

17. Seminar Schedule – Remainder of Morning
10:00 – 10:30 Physical Laboratory Visit
(Room 103, 251 Mercer St.)
(see NYU Map Handout for details)
10:30 – 11:30 MATLAB Computing Exercises
(Break into Groups of Two)
(Room 305, 197 Mercer St.)
11:30 – 12: Group Presentations
(Answers to MATLAB Exercises)