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

3. 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. 4 Introduction to Lecture n Atmospheric & Oceanic Flows n Planetary Scale Flows – Feature Tracking n Laboratory Scale Flows – Particle Image Velocimetry n Cross Correlation Analysis n MATLAB Implementation – Particle Image Velocimetry

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

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

7. 7 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.ab Planetary Scale Flows – Feature Tracking

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

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

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

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

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

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

14. 14 MATLAB Implementation – Particle Image Velocimetry (PIV)

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

16. 16 Concluding Remarks– 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 http://fish.cims.nyu.edu/educational_pages/frn_2003/syllabus.html  (see Handout)

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

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