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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. Seminar Schedule . 09:00 – 10:00 Lecture – Cross Correlation

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understanding atmospheric oceanic flows laboratory application of cross correlation

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
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
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
Atmospheric Flows
  • Jet Stream(Discovery Video)
  • Hurricane
  • Tornado
oceanic flows
Oceanic Flows
  • Great Conveyor Belt
  • Gulf Stream
  • Further Information: Read Chapter 1 of Handout: The Oceans and Climate by Bigg
slide7

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.

slide8

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 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

Also use notation ‘*’ to indicate convolution

Cross Correlation Analysis – Basic Concepts
  • One-Dimensional Example

(Convolution, but similar to Cross Correlation)

cross correlation analysis image displacement
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 convolution theorem
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.
concluding remarks cross correlation
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
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
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)