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Understanding Atmospheric and Oceanic Flows: Cross-Correlation Laboratory Applications

Join David M. Holland from NYU's Courant Institute for an engaging seminar on atmospheric and oceanic flows. Explore advanced topics such as feature tracking, particle image velocimetry, and cross-correlation analysis. This hands-on session includes MATLAB computing exercises where attendees can apply learned concepts in real-time. The seminar also covers significant weather phenomena like jet streams, hurricanes, and oceanic currents. Enhance your understanding with interactive demonstrations and collaborative group presentations.

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Understanding Atmospheric and Oceanic Flows: Cross-Correlation Laboratory Applications

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  1. 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

  2. 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)

  3. 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

  4. Atmospheric Flows • Jet Stream(Discovery Video) • Hurricane • Tornado

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

  6. 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.

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

  8. 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

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

  10. 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

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

  12. 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.

  13. MATLAB Implementation –Particle Image Velocimetry (PIV)

  14. 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

  15. 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)

  16. 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)

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