andrea schumacher 1, mark demaria 2 and john knaff 2 1. cira/csu, fort collins, co...

Another Look at the Use of Maximum Potential Intensity

of Tropical Cyclones

Andrea Schumacher1, Mark DeMaria2 and John Knaff2

1. CIRA/CSU, Fort Collins, CO ([email protected])

2. NOAA/NESDIS/StAR, Fort Collins, CO

AMS 30th Conference of Hurricanes and Tropical MeteorologyPonte Vedra, FL16-20 April 2012

Outline

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

Use of MPI in SHIPS

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

POT2 is also an important predictor in SHIPS Negative coefficient, reduces influence, especially

for weak systems with large MPI

Empirical MPI

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,T0 = 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)

C0 = -79.17 ms-1, C1 = 5.36 ms-1

SST in °C EPMPI given in ms-1

Why use empirical MPI?

Function of SST only (simple) Works well in SHIPS (top predictor) Assumptions for theoretical MPI not always valid Vmax > MPI

62506

62512

62518

62600

62606

62612

62618

020406080

100120140160

0

10

20

30

40

50

60

Hurricane Celia 2010

VMAX EMP MPIEMANUEL MPI OHC

Vm

ax (

kt)

OH

C (k

J/cm

2)

Example: Hurricane Celia 2010

Main limitation = Empirical does not take into account structure atmosphere.Prefer to use theoretical MPI in SHIPS.

Empirical vs. Theoretical MPIAtlantic 1982-2011 (SHIPS)

Vmax > MPI91 of 9923 cases

(0.9%)

Empirical MPI (DeMaria and Kaplan 1994)

Theoretical MPI (Emanuel 1985, 1994, 1995)


(6.9%)

Idea: What if we “correct” cases where Vmax > theoretical MPI?

Initial corrections

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)


(4.1%)

Initial corrections(Speed and boundary layer reduction)

Theoretical MPI (Emanuel)


(6.9%)

Diagnosing/Predicting Cases where Vmax > MPI Linear Discriminant Analysis Locate pre-ET cases

PredictorNormalize

d Coefficient

Latitude 0

SST -4.8

V500 0.8

V300 -1.2

850-mb Temp Gradient 0.5

T150 -0.9

850-200 mb Vertical Shear -0.7

Northward Motion 1.2

Obs Yes

Obs No

Pred Yes

321 72

Pred No

84 9446

POD = 79.3%FAR = 0.8%

Annular hurricanes may also exceed current MPI (use AH Index parameters)

Hybrid MPI (Theoretical-Empirical)


(1.0%)

Hybrid MPITheoretical MPI (Emanuel)


(6.9%)

Can we replace empirical MPI with hybrid MPI (mostly theoretical) in SHIPS?

HMPI = EMPI where Vmax > TMPI

HMPI = TMPIelsewhere

Evaluating hybrid MPI

Both theoretical MPI and hybrid MPI improve r2 in simple model (hybrid better)

Both decrease r2 in SHIPS (more independent variables complicate statistical relationship)

Evaluating hybrid MPI (cont…)

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 POT2 predictors

Evaluating empirical MPI + theoretical MPI

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

Simple MLR – coefficient values

•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

POT POT2 HPOT HPOT2

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

dVmax = a(POT) + b(POT2) + c(TPOT) + d(TPOT2) + e

Empirical only Empirical + Hybrid

Coeffi

cie

nt

valu

e

Evaluating empirical MPI + theoretical MPI (cont…)

VMAX

ADAY

PSLV

PC20 PO

TT2

00EP

OSTW

TD20

0

VSHR

RHCN

SHGC

TPOT

-1

-0.5

0

0.5

1

1.5

48-hr Coefficients

Empirical Empirical + Theoretical

Empirical terms Theoretical terms

Why the switch in sign? Interacting with other predictors? Needs more follow up.

Wrap-up

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 r2 (fit), but adding it increases r2

Wrap-up (cont…)

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

andrea schumacher 1, mark demaria 2 and john knaff 2 1. cira/csu, fort collins, co...

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