Understanding Atmospheric & Oceanic Flows: Laboratory Application of Cross-Correlation

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 – 12:00 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. Also use notation ‘*’ to indicate convolution Cross Correlation Analysis – Basic Concepts • One-Dimensional Example (Convolution, but similar to Cross Correlation)

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 • http://fish.cims.nyu.edu/educational_pages/frn_2003/syllabus.html • (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 – 12:00 Group Presentations (Answers to MATLAB Exercises)