1. Andrea Schumacher 1, Mark DeMaria 2 and John Knaff 2 1. CIRA/CSU, Fort Collins, CO (schumacher@cira.colostate.edu) 2. NOAA/NESDIS/StAR, Fort Collins, CO AMS 30 th Conference of Hurricanes and Tropical Meteorology Ponte Vedra, FL 16-20 April 2012

2.  Overview of use of maximum potential intensity (MPI) in the Statistical Hurricane Intensity Prediction System (SHIPS)  Limitations of using empirical MPI  Approaches to using theoretical MPI in SHIPS  Replacing empirical with theoretical  Adding theoretical as complementary term  Summary & future work

3. SST Potential (POT) = MPI – Vmax(t=0)  MPI is the along-track average of empirically estimated MPI  POT is the most important predictor in SHIPS  Positive coefficient  POT 2 is also an important predictor in SHIPS  Negative coefficient, reduces influence, especially for weak systems with large MPI

4.  Atlantic (DeMaria and Kaplan 1994)  Clim SST/Vmax sample from 1962-1992  Fit upper bound of Vmax (least squares, exponential)  A = 28.2, B = 55.8, C = 0.1813,T 0 = 30.0 °C  SST in °C  V given in ms-1  E. Pacific (Whitney and Hobgood 1997)  Clim SST/Vmax sample from 1963-1993  Fit upper bound of Vmax (least squares, linear)  C 0 = -79.17 ms -1, C 1 = 5.36 ms -1  SST in °C  EPMPI given in ms -1

5.  Function of SST only (simple)  Works well in SHIPS (top predictor)  Assumptions for theoretical MPI not always valid  Vmax > MPI Example: Hurricane Celia 2010 Main limitation = Empirical does not take into account structure atmosphere. Prefer to use theoretical MPI in SHIPS.

6. Vmax > MPI 91 of 9923 cases (0.9%) Empirical MPI (DeMaria and Kaplan 1994) Theoretical MPI (Emanuel 1985, 1994, 1995) Vmax > MPI 686 of 9923 cases (6.9%) Idea: What if we “correct” cases where Vmax > theoretical MPI?

7. Corrected MPI for asymmetries due to forward motion (Schwerdt et al. 1979) Used updated 700 mb to boundary layer reduction factor (0.9, Franklin et al. 2002) Vmax > MPI 405 of 9923 cases (4.1%) Initial corrections (Speed and boundary layer reduction) Theoretical MPI (Emanuel) Vmax > MPI 686 of 9923 cases (6.9%)

8.  Linear Discriminant Analysis  Locate pre-ET cases Predictor Normalized Coefficient Latitude0 SST-4.8 V5000.8 V300-1.2 850-mb Temp Gradient0.5 T150-0.9 850-200 mb Vertical Shear -0.7 Northward Motion1.2 Obs YesObs No Pred Yes 32172 Pred No 849446 POD = 79.3% FAR = 0.8% Annular hurricanes may also exceed current MPI (use AH Index parameters)

9. Vmax > MPI 100 of 9923 cases (1.0%) Hybrid MPI Theoretical MPI (Emanuel) Vmax > MPI 686 of 9923 cases (6.9%) Can we replace empirical MPI with hybrid MPI (mostly theoretical) in SHIPS? HMPI = EMPI where Vmax > TMPI HMPI = TMPI elsewhere

10.  Both theoretical MPI and hybrid MPI improve r 2 in simple model (hybrid better)  Both decrease r 2 in SHIPS (more independent variables complicate statistical relationship)

11.  Replacing empirical MPI with theory-based MPI has negative effect on skill of SHIPS  SHIPS does not have an explicit SST predictor, only POT  Different approach – instead of replacing empirical MPI term, keep it and add a theoretical MPI term  Use the POT and POT 2 predictors

12.  Adding hybrid MPI and independent variables improves the fit of both the simple MLR model and SHIPS (very small)

13. Positive contributions from both empirical and theoretical MPI potential terms Negative contributions from both squared potential terms Essentially split contribution from MPI potential into empirical and theoretical components

14. Empirical terms Theoretical terms Why the switch in sign? Interacting with other predictors? Needs more follow up.

15.  Summary  Attempted to replace empirical MPI in SHIPS with a more theory-based formulation (Emanuel)  Developed an LDA model to diagnose cases where Vmax > theoretical MPI (POD = 80%, FAR = 1%)  Defined a hybrid MPI (HMPI): ▪ Where Vmax > theoretical MPI, HMPI = empirical MPI ▪ HMPI = theoretical MPI elsewhere  Simple MLR model suggests theoretical/hybrid MPI has higher correlation with dVmax than empirical MPI  In SHIPS, replacing empirical MPI with theoretical/hybrid MPI decreases r 2 (fit), but adding it increases r 2

16.  Future work  Determine what the MPI should be for cases where Vmax > theoretical MPI (early ET, annular cases, etc)  Closer look at how theoretical MPI potential terms are impacting SHIPS ▪ Simple MLR model results encouraging, physical ▪ Coefficient signs are the reverse of expected in SHIPS