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A PREFERRED SCALE FOR WARM CORE INSTABILITIES IN A MOIST BASIC STATE Brian H. Kahn J P L Doug Sinton S J S U Meteorology Friday June 8, 2007. TITLE. SUB SYNOPTIC SCALE INSTABILITY AND HURRICANE PRECURSORS Doug Sinton SJSU Meteorology Wednesday May 2, 2007. Model

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title

A PREFERRED SCALE FOR WARM CORE INSTABILITIES IN A MOIST BASIC STATE

BrianH.Kahn

JPL

DougSinton

SJSUMeteorology

Friday June 8, 2007

TITLE
  • SUB SYNOPTIC SCALE INSTABILITY AND HURRICANE PRECURSORS
  • Doug Sinton
  • SJSU Meteorology
  • Wednesday May 2, 2007
abstract
Model

linear two-layer shallow water Orlanski (1968)

simple parameterized latent heat release

Conditions

moderate to weakly baroclinic

near moist adiabatic

Results

most unstable mode: warm-core

maximum growth rates ~ 0.46f

Ro of most unstable mode ~ 0.9 for 10 < Ri < 1000

for given static stability preferred scale varies as Ri-1/2

Implications

organize convection in tropical cyclone precursors

account for tropical cyclone and polar low scale

ABSTRACT
observation detail
Frank and Roundy 2006 O

BS DET

Statistical correlation

Tropical waves precede tropical cyclogenesis

Four types of tropical cyclone precursors

Rossby-Gravity, Baroclinic, Equatorial Rossby, MJO

Produce favorable conditions for tropical cyclogenesis

Common structure

Flow reversal aloft

Baroclinic first internal vertical mode

Moore and Haar 2003

OBSERVATION DETAIL

Polar Low

warm core structure

OBSERVATIONDETAIL
slide8
CISK

Hypothesis

  • Convective heating induces sub-synoptic circulation
  • Circulation converges water vapor needed by convection

Deficiencies

  • Convective vs sub-synoptic scale mismatch
  • CAPE redistributes moist static energy without replenishing it
  • CAPEUltra-violetcatastropheCISKCIFK
wishe
WISHE

Hypothesis

  • SST source of sufficientmoist static energy
  • Windenhancesevaporative water vapor fluxfromocean
  • Saturated boundary layeraids/sustainsconvection
  • Enhanced convective heatingstrengthens wind

Deficiency Motivation

  • SCALEof wind circulationNOT accounted for
hypothesis details
Hypothesis: test for linear instability

Is there a preferred scale?

If so, what is its structure?

If so, what are controlling processes and conditions?

Methodology: simple model

Two layer shallow water model

permits range of instabilities

First internal vertical mode: feasibility of simple LHR scheme

Non quasi-geostrophic approach

Short wave scale violation problem avoided

Ageostrophic thickness advection permits warm core structure

Caveats

Not a simulation

Not only explanation for development

HYPOTHESIS DETAILS
g vs ag temp adv warm core

G

GEOvsAGEOTEMPADV FORWARMCORE

G vs AG TEMP ADV warm core

AG

P2

C

T =P2–P1

W

P1

z

y

x

latent heat parameterization cases

LATENT HEAT PARAMETERIZATION CASES

-Q*DIV

-(1-Q)DIV

-DIV

Q > 0.5

AVG DENSITY

DECREASES

“WARMING”

Q = 0

AVG DENSITY

INCREASES

“COOLING”

Q = 0.5

AVG DENSITY

UNCHANGED

“CONSTANT”

INITIAL

DIV< 0

model energetics schematic
MODEL ENERGETICS SCHEMATIC

ZAPE

WBC

WK

EAPE

EKE

WQ

qg short wave cutoff q 0
QGSHORT WAVE CUTOFFq = 0

ZAPE

WBC

WK

EAPE

EKE

Ro

cisk energetics q 0 5
CISK ENERGETICSq > 0.5

ZAPE

WBC

WK

EAPE

EKE

Ro

WQ

wishe energetics q 0 5
WISHE ENERGETICSq0.5

ZAPE

WBC

WK

EAPE

EKE

WQ

Ro

eigenvalue problem
EIGENVALUE PROBLEM

Newton - Raphson confirms eigenvalues

phase lags t p 2 p 1

P2

PHASE LAGS T=P2–P1

T

P1

90°

180°

-90°

energy vector
ENERGY VECTOR

WBCG

WBCAG

-WBCG

WBCAG

-WBCAG

WBCG

WBC > WQ

WQ > WBC

warm core circulation

WARMCORECIRCULATIONqc ~ 0.49 Ro ~ 0.9

WARM CORE CIRCULATION

LARGE Ro X – Z CIRCULATION

P2

C

C

W

W

T

P1

z

y

x

conclusions
Model

linear two-layer shallow water

simple parameterized latent heat release

Conditions

weakly baroclinic

near moist adiabatic

Results

warm-core: most unstable mode for nearly saturated conditions

growth rate sensitive to saturation not Ri

instabilities limited to Ro < 1.5

preferred scale determined by (vertical shear)1/2

Implications

Organize and pre-condition convection associated with hurricane and polar low development

account for hurricane and polar low scale

weaker shears favor development as smaller preferred scales more likely to be saturated

stronger shears stabilize shorter scales

CONCLUSIONS
w h a t s n e x t
WHAT’SNEXT?
  • Make model non-frontal
  • Add horizontal shear
  • Nonlinear with random initial perturbation
acknowledgment professor c r mechoso and professor a arakawa
ACKNOWLEDGMENTProfessor C. R. MechosoandProfessor A. Arakawa
  • Once a UCLA Atmos Science grad student
  • Always a UCLA Atmos Science grad student
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