1. OPERATIONAL IMPLEMENTATION OF AN OBJECTIVE ANNULAR HURRICANE INDEX ANDREA B. SCHUMACHER 1, JOHN A. KNAFF 2, THOMAS A. CRAM 1, MARK DEMARIA 2, JAMES P. KOSSIN 3 1 CIRA, Colorado State University, Fort Collins, CO 2 NOAA/NESDIS, Fort Collins, CO 3 CIMSS, University of Wisconsin-Madison, Madison, WI

2. 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)

3. 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)

4. 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)

5. 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

6. Determining Annular Structure Subjective DiagnosticObjective ParameterSource Large eyewall radiusRcRc IR Imagery Warm Eye Δ T eye IR Imagery Vertical shearSHRDNCEP analysis 200 hPa windsU200NCEP analysis Eddy flux convergenceREFCNCEP analysis SST Reynolds SST Intensity NHC Best Track Yellow = Structure Blue = Environment

7. Annular Hurricane Index (AHI)

8. AHI Step 1: Screening ParameterPrescreening Criterion Intensity< 84 kt RcRc <50 km Δ T eye < 15 o C SHRD>11.3 ms -1 U200 1.5 ms -1 REFC 11 ms -1 day -1 SST 29.1 o C +/- 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%

9. AHI Step 2: Linear Discriminant Analysis (Overview)  Graphical Interpretation of LDA for Case With 2 Predictors (x,y) and 2 Groups DF=0 DF = c 0 + c 1 x + c 2 y Coordinate transformation that provides maximum separation of groups (From www.doe-mbi.ucla.edu) Refs: Wilks (2006), Hennon & Hobgood (MWR, 2003)

10. 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 R c  VAR – variance of azimuthally-averaged BTs from TC center to 600 km  ΔT eye - max difference between R c and any azimuthally-averaged BT at smaller radius ** exceeds 95% confidence level using Student’s T test

11. Verification  Dependent Years (1995-2003)  Independent Years (2004-2006) 467 56132 AH “Y” AH “N” LDA “Y”LDA “N” 70 1461 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:

12. 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

13. 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

14. AHI Output Displayed at End of SHIPS Model Output File ** *ANNULAR HURRICANE INDEX* *EP EP052006 07/22/2006 00 UTC* ** SCREENING STORM INTENSITY=130kt>84kt ?--->PASSED SCREENING SST=27.3C>24.3°C ?--->PASSED SCREENING SST=27.3C<29.1°C ?--->PASSED SCREENING VERTICAL SHEAR=5.7kt<21.97kt ?--->PASSED SCREENING 200 hPa ZONAL WIND=-13.2kt>-22.94kt ?--->PASSED SCREENING 200 hPa ZONAL WIND=-13.2kt<2.92kt ?--->PASSED SCREENING 200 hPa MOM FLUX CONV=-0.1m/s-day>-9m/s-day ?--->PASSED SCREENING 200 hPa MOM FLUX CONV=-0.1m/s-day<11m/s-day ?--->PASSED SCREENING GOES RAD COLD BR TEMP=106km>50km ?--->PASSED SCREENING GOES EYE-RING BR TEMP=66.2C>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)* *****************************************************************************

15. 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