# Presentation: 344028

## OPERATIONAL IMPLEMENTATION OF AN OBJECTIVE ANNULAR HURRICANE INDEX ANDREA B. SCHUMACHER1, JOHN A. KNAFF2, THOMAS A. CRAM1, MARK DEMARIA2, JAMES P. KOSSIN3

- 1CIRA, Colorado State University, Fort Collins, CO
- 2NOAA/NESDIS, Fort Collins, CO
- 3CIMSS, University of Wisconsin-Madison, Madison, WI

## Overview

- Annular hurricanes:  structural characteristics
- General environmental conditions
- Intensity characteristics:  Motivation for objective prediction scheme
- Objectively determining annular structure: Annular Hurricane Index
- Step 1: Screening
- Step 2: Linear discriminant analysis
- Verification
- Operational example:  Daniel 2006 (EP05)

## Annular Hurricane Structure

-  Distinctly axisymmetric
-  Large circular eyes
-  Greatly reduced rainband activity
-  Lasts at least 3 hours
- Rare, occur ~4% of the time

*Isabel (2003)*

## Environmental Conditions

- Weak Easterly/Southeasterly Wind Shear
- Weak Relative Eddy Flux Convergence
- 200 hPa Easterlies
- SSTs in a range 25.4 to 28.6 °C steady or decreasing.
**OR**
- Weak Easterly shear, under an upper ridge, over SST <28.6 °C
**ALSO**
- Intensity > 85 kt
**(*****Knaff et al. 2003*****)**

## Annular Hurricane Intensity Characteristics

- Do not weaken rapidly after max intensity
- Intensity is very close to 85% MPI wrt SST
- Have large intensity biases & larger than normal intensity errors

**Notes:**
Motivation – especially last bullet

## Determining Annular Structure

| Subjective Diagnostic | Objective Parameter | Source |
| --- | --- | --- |
| Large eyewall radius | Rc | IR Imagery |
| Warm Eye | ΔTeye   | IR Imagery |
| Vertical shear | SHRD | NCEP analysis |
| 200 hPa winds | U200 | NCEP analysis |
| Eddy flux convergence | REFC | NCEP analysis |
| SST | SST | Reynolds SST |
| Intensity | Intensity | NHC Best Track |

- Yellow = Structure                                        Blue = Environment

**Notes:**
Knaff et al 2003 suggested using structural and environmental characteristics to develop object AH IDs

Rc = radius of coldest azimuthally-avg temps
ΔTeye = max difference between Rc and any azimuthally-avg temp at smaller radius
SHRD = 850-200 mb deep layer vertical shear
U200 = 200 hPa winds

## Annular Hurricane Index (AHI)

**Notes:**
From ideas of K03, developed the AHI

## AHI Step 1: Screening

| Parameter | Prescreening Criterion |
| --- | --- |
| Intensity | < 84 kt |
| Rc | <50 km |
| ΔTeye   | < 15 oC |
| SHRD | >11.3 ms-1 |
| U200 | < -11.8  or > 1.5 ms-1 |
| REFC | < -9 or >  11 ms-1 day-1 |
| SST | <24.3  or > 29.1 oC |

- +/- 3 standard deviations from means of AH’s (1995-2003)
- 976 (54 AH) cases (6h) > 84 kt intensity  241 cases after screening (53 AH)
- Hit Rate = 100%,  False Alarm Rate = 19%

**Notes:**
1995-2003 development dataset cut down from 976 to 241 pts (53 obj id’d as annular)
1995-2003 AH mean vals +/- 3 std dev
100% hit rate, 19% false alarm (Mason & Graham 1999)
LDA  improve false alarm rate

## AHI Step 2: Linear Discriminant Analysis (Overview)

**Graphical Interpretation of LDA for Case With 2 Predictors (x,y) and 2 Groups**

- DF=0

- DF = c0 + c1x + c2y
- Coordinate transformation that provides maximum separation of groups
*(From www.doe-mbi.ucla.edu)*

- Refs:  Wilks (*2006*), Hennon & Hobgood (*MWR, 2003*)

**Notes:**
When you have 2 groups and k predictors
Discrim Function is linear combination of the k predictors
LDA used to take advantage of the differences in predictor dist/means between annular and non-annular groups
Predictors used that had significance diff in means between 2 groups

## AHI Step 2: Linear Discriminant Analysis (cont...)

- Only predictors with significant annular vs. non-annular differences in means were used**
- SST
- U200 – 200 hPa zonal winds
- σ c – azimuthal standard deviation of BTs at Rc
- VAR – variance of azimuthally-averaged BTs from TC center to 600 km
- ΔT eye - max difference between Rc and any azimuthally-averaged BT at smaller radius
***** exceeds 95% confidence level using Student’s T test*

## Verification

- Dependent Years (1995-2003)
- Independent Years (2004-2006)

| 46 | 7 |
| --- | --- |
| 56 | 132 |

- AH “Y”

- AH “N”

- LDA “Y”

- LDA “N”

| 7 | 0 |
| --- | --- |
| 14 | 61 |

- AH “Y”

- AH “N”

- LDA “Y”

- LDA “N”

- Hit Rate ~ 87 %
- FA Rate ~   6 %

- Hit Rate ~ 100 %
- FA Rate ~     4 %

**STEP 1:**
- _Screening_
- Reduced 941 (54) cases to 241 (53)
- FAR = 19%

**STEP 2:**

**STEP 1:**
- _Screening_
- Reduced 387 (7) cases to 82 (7)
- FAR = 19%

**STEP 2:**

**Notes:**
1995-2003 after screening, HR = 100%, FAR = 19% ..... Got FAR down to 6% with LDA
LDA not perfect – decreased HR
1995-2006: Hit Rate = 96%, False Alarm Rate = 6%

LDA meant to be a “yes” or “no” predictor of group membership
However, we can assign probabilities to various dicrim values based on 1995-2003 sample groups  AH Index

## AHI Output & Interpretation

- If case doesn’t pass screening, AHI set to 0.
- If screening is passed, LDA function value is linearly scaled to obtain the Annular Hurricane Index, which ranges between 1 & 100.
- AHI is displayed at the end of the SHIPS model output file.
-    AHI = 0      No annular structure
-    AHI = 1      Worst match to annular structure
-    AHI = 100  Best match to annular structure

**Notes:**
Discrim range from -2.3 to -0.3
Linear scaling corresponds to 96% hit rate and 6% false alarm rate in developmental data (95-06, 1363 possible cases)
~ 47% of false alarms becoming annular or had just been annular

## Example:  Daniel 2006

- 7/20/06 0Z, vmax=95 kt
- AHI =  0

- 7/21/06 0Z, vmax=120 kt
- AHI =  50

- 7/22/06 0Z
- vmax = 130 kt
- AHI =  100

## AHI Output Displayed at End of SHIPS Model Output File

| * |  |  |  |  |  |  |  | * |
| --- | --- | --- | --- | --- | --- | --- | --- | --- |
| * | ANNULAR HURRICANE INDEX |  |  |  |  |  |  | * |
| * | EP    EP052006  07/22/2006 00 UTC |  |  |  |  |  |  | * |
| * |  |  |  |  |  |  |  | * |
| SCREENING STORM INTENSITY | = | 130 | kt | > | 84 | kt ? | ---> | PASSED |
| SCREENING SST | = | 27.3 | C | > | 24.3 | °C ? | ---> | PASSED |
| SCREENING SST | = | 27.3 | C | < | 29.1 | °C ? | ---> | PASSED |
| SCREENING VERTICAL SHEAR | = | 5.7 | kt | < | 21.97 | kt ? | ---> | PASSED |
| SCREENING 200 hPa ZONAL WIND | = | -13.2 | kt | > | -22.94 | kt ? | ---> | PASSED |
| SCREENING 200 hPa ZONAL WIND | = | -13.2 | kt | < | 2.92 | kt ? | ---> | PASSED |
| SCREENING 200 hPa MOM FLUX CONV | = | -0.1 | m/s-day | > | -9 | m/s-day ? | ---> | PASSED |
| SCREENING 200 hPa MOM FLUX CONV | = | -0.1 | m/s-day | < | 11 | m/s-day ? | ---> | PASSED |
| SCREENING GOES RAD COLD BR TEMP | = | 106 | km | > | 50 | km ? | ---> | PASSED |
| SCREENING GOES EYE-RING BR TEMP | = | 66.2 | C | > | 15 | °C ? | ---> | PASSED |
|  |  |  |  |  |  |  |  |  |
|  | STORM MAY BE ANNULAR, PASSED SCREENING |  |  |  |  |  |  |  |
|  | CALCULATE AHI FROM DISCRIMINANT ANALYSIS |  |  |  |  |  |  |  |
|  |  |  |  |  |  |  |  |  |
| * | *************************************************************************** |  |  |  |  |  | * |  |
| * |   ANNULAR HURRICANE INDEX (AHI) VALUE = 100. |  |  |  |  |  | * |  |
| * |   (AHI = 100.      IS BEST MATCH TO ANNULAR STRUCTURE) |  |  |  |  |  | * |  |
| * |   (AHI =     1.   IS WORST MATCH TO ANNULAR STRUCTURE) |  |  |  |  |  | * |  |
| * |   (AHI =     0.                           FOR NO ANNULAR STRUCTURE) |  |  |  |  |  | * |  |
| * | *************************************************************************** |  |  |  |  |  | * |  |

**Notes:**
At end of SHIPS text output file

Screening values only shown if screening passed

## Summary

- AHI is an objective algorithm that determines the likelihood of annular structure in an existing hurricane using SHIPS environmental predictors and 6-hr storm-centered GOES IR imagery
- For the period 1995-2006, the AHI algorithm had a hit rate of 96% and a false alarm rate of 4%
- The AHI will be tested in a real-time operational setting, running concurrently with the SHIPS model, at the National Hurricane Center during the 2007 hurricane season.
- After the 2007 season, if evaluation of the algorithm is favorable the transition to an operational product will be pursued

**Notes:**
Emphasize that we are looking for feedback, particularly from forecasters