1. AUTOMATED TROPICAL CYCLONE EYE DETECTION USING DISCRIMINANT ANALYSIS
Robert DeMaria

2. Overview Background Motivation Current Method Objective
Proposed Method
Data
Algorithm
Results
Conclusions
Future Work

3. Schematic of a Hurricane Eye
Warm ocean evaporates near ring of very strong winds near the center
2. That causes a ring of thunderstorms near the center called the eye wall. Air moves upward in the eyewall (orange arrows)
3. When storm is organized, air starts to sink in the middle causing clouds to evaporate there and cause the eye to form.
From “Hurricane Science and Society” web page

4. Infrared Image of Hurricane Joaquin October 3, 2015
Note: Coldest areas are bright colors, showing eye wall. Clear area near the storm center is the eye.

5. Why Do We Care About Detecting Hurricane Eyes?
Initial eye formation is a sign a tropical cyclone is getting more organized
It is often a signal that the storm is about to get much stronger
Eye detection is an important step in estimating the current strength of a hurricane

6. Current Methods Hurricane hunter aircraft Dvorak Technique
sos.noaa.gov/Education/tracking.html
Hurricane hunter aircraft
Low availability
Dvorak Technique
Used world wide
Produces TC intensity estimates from satellite imagery
Determining if a storm has an eye is an important step in the Dvorak technique
Performed every 6 hours

7. Dvorak Technique for Intensity Estimation
Uses both human judgment (with strict criteria) and automated tools
Forecaster examines visible/IR/microwave imagery
Forecasters subjectively classify satellite image as one of 4 basic patterns
Curved band
Shear pattern
Central Dense Overcast
Eye
Properties of pattern determine intensity
IE: Thickness of eyewall
Size of curved band, size of CDO

8. Dvorak cont.
Eye pattern selected if there is region near rotational center devoid of clouds
Manual processes are time consuming
Only small fraction of satellite data is used

9. Objective
Replicate human-performed eye detection with automated procedure
Utilize same input routinely available to forecasters
Make eye detection available at more times to supplement human-performed eye detection.

10. Proposed Method Use geostationary IR data and best track data.
Use simple statistical computer vision/machine learning techniques
Principal Component Analysis (PCA)
Linear Discriminant Analysis (LDA)
Quadratic Discriminant Analysis (QDA)
Use archive of classified images (from Dvorak) as training/truth.

11. Infrared Data from Geostationary Satellites
2D Image of cloud-top temperature
Available every 30 minutes around the globe

12. IR vs Microwave vs Visible
Used in addition to IR in Dvorak.
Only available during the day.
Adds complexity to algorithm.
Microwave
3D view inside storm.
Easier to determine if eye is present.
Only available every 12 hr per satellite.
Microwave channels vary between satellites.
Can miss a storm entirely.

13. Storm “Best Track” Estimates of storm position and maximum wind speed
Updated every 6 hours from satellite and aircraft data

14. Seven Variables Used From Best Track
Position:
Motion Vector:
Max Wind Speed:
Date:

15. Dvorak Classifications
data from CIRA archive
4109 samples at 6 hr intervals
Atlantic only
991 (24%) eye cases

16. A Note About “Truth”
Dvorak method has some flexibility for forecasters to interpret what they see.
Using these classifications as truth will replicate any biases present in the Dvorak classifications.

17. Algorithm Subsect/unroll satellite imagery Form training/testing sets
Perform PCA for dimension reduction
Select predictors (using sensitivity vector)
Train QDA/LDA
Use testing set to evaluate performance

18. Three Versions of Algorithm
Model 1
Best track input only
Model 2
IR satellite data only
Model 3
Combined best track and IR data
Use sensitivity vector (defined later) to pick best set of predictors

19. Step 1) Subsecting Imagery
Cut out 80x80 pixel box centered on best track estimate.
320km x 320km

20. Unroll Imagery
Unroll 80x80 pixel box to form 6400 element vector.

21. Step 2) Training/Testing Sets
Data randomly shuffled
70% used for training
30% used for testing
Great care taken not to bias results using testing data.

22. Normalization
Subtract mean image.
Divide by standard deviation image.

23. Problem Have 4109 total samples and 6400 dimensions per image
Solution: Use PCA to reduce data to most important patterns.

24. Step 3) Principal Component Analysis
PCA generates an eigenvector for each dimension (6400 total)
Eigenvalues represent variance explained by each eigenvector

25. Dimension Reduction
~95%
Can select subset of eigenvectors (based on variance explained).
Can project data on to subset to reduce dimension of data.
IE: 6400 element vector becomes 25 element vector.

26. First 25 Eigenvectors
7 & 8 curved band

27. Dimension Reduction
Can construct approximation of original data with a few EOFs

28. Step 4) Select Predictors
Model 1
7 Best track predictors
Model 2
25 IR EOF predictors with highest variance explained
Model 3
Sensitivity vector used to select best predictors
10 IR EOF predictors
4 Best track predictors

29. Step 5) QDA/LDA Discriminant Functions
where Σk is the covariance matrix for class k and μk is the mean for class k.
LDA:
where Σ is the weighted average of all Σk.
Pick class k with the largest δk value
Bi-variate normal distributions provide probability of being in class k

30. Sensitivity Vector
Use LDA to give insight into importance of predictors
Calculate change of discriminate function difference with 1 standard deviation change in each predictor value z
∆z(δ2-δ1) = ∂/∂z[(δ2-δ1)]z
LDA δk are linear in x, so ∆z are constants

31. Step 6)Evaluation of Performance
Confusion matrix related metrics
Fraction Correct
True Positive Fraction
True Negative Fraction
False Positive Rate
False Negative Rate

32. Additional Metrics Peirce Skill Score (PSS) Brier Skill Score (BSS)
Evaluates skill of classification compared to random guesses based on training data distrib.
Brier Skill Score (BSS)
Evaluates skill of probabilities compared to constant probabilities obtained from training data distrib.
BSS and PSS
1 is perfect
0 is no better than no skill scheme
< 0 is worse than no skill.

33. Model 1 Used only information derived from best track
lat, lon, vmax, Julian Day
Storm velocity, previous change in max winds
Compared QDA and LDA metrics
Used sensitivity vector to understand results

34. Best Track Predictor Distributions look for differences between classes

35. Model 1Performance Metrics
Notes: About 85% correct, BSS better for LDA, PSS tiny bit better for QDA

36. Sensitivity Vector for Model 1
Note: Sign provides physical insight. For example, stronger storms or higher latitude storms more likely to have an eye.

37. Two-Predictor Model Pick top two predictors from sensitivity matrix
Vmax and lat
Verification only a little worse than w\ 7 predictors
Plot class boundaries to compare QDA/LDA
Most of signal is in vmax
QDA helps to keep middle latitude cases in but exclude very low and high latitude cases

38. Model 2 – Satellite data only
Input amplitudes (PCs) for top 25 EOFs
Performance not as good as Model 1
Sensitivity vector shows which patterns help divide classes

39. Sensitivity Vector for Model 2

40. Top 4 EOFs for Model 2
Note that top 4 are all very symmetric. Negative sign of sensitivity vector for 9, 4, 15 accounts for the fact that the cold part is in the middle.

41. Model 3 – Combined IR and Best Track
Want to keep number of predictors small
Pick predictors where sensitivity vector is about 20% or more of most important predictor
4 Best Track predictors
Vmax, lat, eastward and northward motion
10 IR predictors

42. Model 3 Verification Results
About 90% correct classification (close to 95% accuracy of “truth”)
BSS better for LDA (accuracy of probabilities)
PSS better for QDA (accuracy of classifications)
QDA has fewer samples for eye covariance matrix.
Note use of all data for case studies.
Average Performance metrics from 1000 shufflings of training/testing sets and with all cases

43. Sensitivity Vector for Model 3
Max wind is top, but IR data are the next three

44. Class Boundaries for Two-Predictor Model Vmax and IR EOF1
Right hand side isn’t really doing anything
Left hand side curve does a better job of classifying weak cases.

45. Case Study Analysis Pick weak, moderate and strong cases
Arlene 2005, Danielle 2010, Katrina 2005
Use full sample to make sure all cases for each storm included
Plot classifications, probabilities and truth for full life cycle
Examine cases where method failed

46. Algorithm Analysis for Hurricane Daniellex x

47. Reasons for Mis-Classifications
Center position was not accurate
Possible fix by repositioning
Cold clouds were displaced from center, usually due to wind shear
Wind shear vector is known, use as additional input or to rotate coordinates of IR data

48. Conclusions
LDA and QDA can be used to objectively identify tropical cyclone eyes using commonly available data
IR satellite imagery and basic storm parameters
90% success rate
LDA is better for estimating probabilities
QDA is better for classification
Most important input is Vmax
IR data more important than all other best track inputs

49. Future Work Develop method to re-center images. Use wind shear data.
Predict eye development using probabilities.
Use output to help with rapid intensification forecasting.
Generalize method to estimate all four Dvorak scene types.

50. Extra Slides

51. Step 5) QDA/LDA
Need estimate of probability of being in class k, given input vector x: P(C=k | x)
Bayes rule relates P(C=k | x) to P(x | C=k)
Fit bivariate normal distributions to get P(x) for each class
Take natural log of P(C=k | x) to get discriminate function for each class
For LDA, assume class covariance matrices are equal
Makes discriminant function linear in x

52. Danielle Misclassified Images
False Positives:
False Negatives:

53. Algorithm Analysis for Hurricane Katrinax x X X

54. Katrina Misclassified Images
False Negatives: