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

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)

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

Atmospheric Flows Jet Stream (Discovery Video) Hurricane Tornado

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

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.

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

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

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

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

Cross Correlation Analysis – Fast Fourier Transform One-Dimensional Example

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.

MATLAB Implementation – Particle Image Velocimetry (PIV)

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

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)

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)