Tropical Cyclone Intensity Estimation using Eigenanalysis Techniques Tim Douglas EGGN 512 – Computer Vision Final Project May 1, 2012 Outline • 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 – 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 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 T used to correlate a test storm A = U D V against for identification. ATA (nxn) is small. • Perform principle component Eigenvectors of ATA are the analysis (PCA) via the singular value columns of V. decomposition (SVD) of the known T storm database matrix A. Eigenvalues of A A are the • Columns of U represent the diagonal entries in D. “eigencanes” of the database. U = A V D‐1 • Project test storm xt onto span(U). Columns of U are the T – Coefficients are: bt = U xt principle components of A • Also compute coefficients for all and eigenvectors of AAT. images in the database. Only keep most significant • Euclidean distance between principle components in U. coefficients quantifies correlation. 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 Vectorized Known Storm Known Storm Database Eigencanes Coefficients 480x480 230400x1 230400x100 230400x20 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)

Closest Match: Stormke H5 .jpg. DIKSS=6.506e+001 Second Match: Stormeanne H 5 .jpg. DIKSS=7.471e+001 Projection of test storm in known storm space I 6 3 J 5 2

Third Match: Stormke H5 .jpg. DIKSS=9.011e+001 Fourth Match: Stormrances TS 5 .jpg. DIKSS=9.089e+001 I 6 2 F 3 3

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 Hurricane Ioke 7 7.3 0.3 Hurricane Edouard 6.5 6.5 0 6.5 6.5 0 6 5.9 0.1 Hurricane Norbert 6 5.9 0.1 Hurricane Bertha 5.5 4.85 0.65 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 4.5 5 0.5 4.5 5.25 0.75 Hurricane Nicole 4.5 4.4 0.1 Tropical Storm Chantal 4 3.9 0.1 Average Error 0.28 Error Variance 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 – 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???