Tropical Cyclone Intensity Estimation using Eigenanalysis Techniques
Tim Douglas
EGGN 512 – Computer Vision
Final Project
May 1, 2012
Outline
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What is the Dvorak Intensity Estimation?
Definition of Intensity Estimation Algorithm
Implementation of Eigenanalysis Techniques
Eigenanalysis – Conceptually & Mathematically
Realization of Eigenanalysis in MATLAB
Test Results and Model Performance
Conclusions
Dvorak Intensity Classification
• 1950’s: Development of visible satellite imaging for weather forecasting and analysis.
• 1960’s: Attempts to estimate cyclone wind speed purely from storm diameter.1
• 1970’s: Meteorologist Vernon Dvorak develops a satellite‐based intensity estimation technique.2
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Eye structure (if one exists)
Curved cloud banding
Relative storm density and structure
Central overcast density
Relative intensity value (CI = T)
1Hubert, Lester F., and Timchalk, Andrew. “Estimating Hurricane Wind Speeds from Satellite Pictures.” Monthly Weather Review, Vol. 97, No.5, pp. 382‐383, 1969.
2Velden, Christopher; et al. “The Dvorak Tropical Cyclone Intensity Estimation Technique.” American Meteorological Society, pp. 1198‐1210, Sept. 2006.
Implementation of Eigenanalysis (1)
• Analyze database of archived storm satellite images over range of intensity values and establish pattern.3
 Most common intensities range from T = 3.5 to 7.5.
 All images 480x480 and span same degrees of latitude/longitude.
 Gamma transform followed by binary thresholding applied to eliminate differences in lighting and hue of satellite images.
• Eigenanalysis employed to determine relative structures of storms within database to form basis manifold.
 Database of 25 storms of known intensities; rotate each image three times (90 degrees each) to enhance rotational symmetry.
 Project test storm image onto basis manifold.
 Estimate intensity based on weighted sum of four nearest neighbors in manifold to location of projection.
3All images archived by National Hurricane Center (NHC), Online: www.nhc.noaa.gov
Implementation of Eigenanalysis (2)
• A database of known storms is used to correlate a test storm against for identification.
• Perform principle component analysis (PCA) via the singular value decomposition (SVD) of the known storm database matrix A.
• Columns of U represent the “eigencanes” of the database.
• Project test storm xt onto span(U).
– Coefficients are: bt = UTxt
• Also compute coefficients for all images in the database.
• Euclidean distance between coefficients quantifies correlation.
A = U D VT
ATA (nxn) is small.
Eigenvectors of ATA are the columns of V.
Eigenvalues of ATA are the diagonal entries in D.
U = A V D‐1
Columns of U are the principle components of A
and eigenvectors of AAT.
Only keep most significant principle components in U.
Eigenanalysis – Conceptually
• “Manifold” refers to multidimensional vector space where principal components of database live (i.e. “eigenspace”).
• Test storm image lives somewhere outside of manifold.
• Compute coefficients of orthogonal projection of test image onto manifold – error is DFSS (distance from storm space)
• Euclidean distance to neighbors is DISS (distance in storm space)
Eigenanalysis – Mathematically
Known Storm
480x480
Vectorized
Known Storm
230400x1
Database
230400x100
Eigencanes
230400x20
Coefficients
20x100
Database Construction – MATLAB
First Eigencane
Second Eigencane
Third Eigencane
Details of Analysis in MATLAB (1)
Hurricane Norbert, T = 6.0
Test Image. DFKSS=2.220e+002
Details of Analysis – MATLAB (2)
Projection of test storm in known storm space
Closest Match: Storm HIke653.jpg. DIKSS=6.506e+001
Second Match: Storm HJeanne552.jpg. DIKSS=7.471e+001
Third Match: Storm HIke652.jpg. DIKSS=9.011e+001
Fourth Match: Storm TSFrances353.jpg. DIKSS=9.089e+001
Ranked Matches: 6.5, 5.5, 6.5, 3.5
Estimated Intensity Weighted Sum: 40%, 30%, 20%, 10%
Estimated Intensity: T = 5.9
Test Results and Model Performance
Storm Name
NHC Dvorak Classification
Model Prediction
Absolute Error
7.5
7.45
0.05
7
7.3
0.3
Hurricane Edouard
6.5
6.5
0
Hurricane Iniki
6.5
6.5
0
Hurricane Marilyn
6
5.9
0.1
Hurricane Norbert
6
5.9
0.1
Hurricane Bertha
5.5
4.85
0.65
Hurricane Charley
5.5
5.9
0.4
Hurricane Roxanne
5.5
5.5
0
Hurricane Carlos
5
5.55
0.55
Hurricane Gert
5
5.6
0.6
Hurricane Frances
4.5
5
0.5
Hurricane Lane
4.5
5.25
0.75
Hurricane Nicole
Tropical Storm Chantal
4.5
4
4.4
3.9
0.1
0.1
Hurricane Gilbert
Hurricane Ioke
Average Error
Error Variance
0.28
0.0676
Conclusions
• Dvorak intensity representation provides an accurate estimation of the strength of tropical cyclones.
• Basic eigenanalysis methods implemented in MATLAB
– Form database of known storms spanning all intensities
– Project unknown storm onto basis manifold
– Four nearest neighbors to projection used in estimation
• Computed using Euclidean distance between coefficients in eigenspace
• Model Performance
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Predicts Dvorak intensity to within +/‐ 0.75 of actual.
Using region properties (EGGN 510): Average error was 0.375.
Weaker storms more difficult due to poorly correlated structure.
Future Improvements: Multiple images of same storm over time, larger database, more precise/consistent preconditioning.
Questions???