TITLE• SUB SYNOPTIC SCALE INSTABILITY AND

HURRICANE PRECURSORS

• Doug Sinton

• SJSU Meteorology

• Wednesday May 2, 2007

A PREFERRED SCALE FOR WARM CORE INSTABILITIES IN A MOIST

BASIC STATE

Brian H. Kahn

JPL

Doug Sinton

SJSU Meteorology

Friday June 8, 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

OBSERVATIONS

Frank and Roundy 2006 OBS 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 2003OBSERVATION DETAIL

• Polar Low– warm core structure

OBSERVATI

ON DETAIL

POLAR LOW

THEORY

CISK FIGURE

< 0

CISK

Conditional Instability of the Second Kind

CAPE

CISKHypothesis• 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• CAPE Ultra-violet catastrophe CISK CIFK

Wind Induced Surface Heat Exchange

WISHE

> 0

WISHE FIGURE

WISHEHypothesis• SST source of sufficient moist static energy• Wind enhances evaporative water vapor flux from

ocean• Saturated boundary layer aids/sustains convection• Enhanced convective heating strengthens wind

Deficiency Motivation• SCALE of wind circulation NOT accounted for

TYPHOON SIZES

HYPOTHESIS METHODOLOGY

LIMITATIONS

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

G vs AG TEMP ADV warm coreP2

T = P2 – P1

P1

C W

AGG GEO vs AGEO TEMP ADV FOR WARM CORE

zy

x

MODEL

MODEL SCHEMATICTWO LAYER SHALLOW WATER MODEL SCHEMATIC

H1

H2

Lx

Ly

H

WARM

COLD

LINEARIZED MODEL EQUATIONS

qq

LATENT HEAT

SCHEMATIC

LATENT HEAT PARAMETERIZATION

-DIV

-Q*DIV

-(1-Q)DIV

INITIAL Q = 0AVG DENSITYINCREASES“COOLING”

Q = 0.5AVG DENSITYUNCHANGED“CONSTANT”

DIV < 0

LATENT HEAT PARAMETERIZATION CASES

Q > 0.5AVG DENSITYDECREASES“WARMING”

ROSSBY NUMBER

Ro

NON DIM MOMENTUM EQN

Ro Ro

Ro

MODEL ENERGETICS SCHEMATIC

ZAPE

EAPE

WBC

WQ

EKEWK

MODEL ENERGETICS

q

QG BAROCLINIC ENERGETICS q = 0

ZAPE

EAPE

WBC

EKEWK

Ro

QG SHORT WAVE CUTOFF q = 0

ZAPE

EAPE

WBC

EKEWK

Ro

CISK ENERGETICS q > 0.5

ZAPE

EAPE

WBC

WQ

EKEWK

Ro

WISHE ENERGETICS q 0.5

ZAPE

EAPE

WBC

WQ

EKEWK

Ro

Newton - Raphson confirms eigenvalues

EIGENVALUE PROBLEM

PHASE LAGS T = P2 – P1

P2

P1

T

0° 90°

180° -90°

RESULTS

ENERGY VECTOR

WBCGWBCAG

-WBCG

-WBCAG

WBC > WQ WQ > WBC

WBCAG

WBCG

GROWTH RATES vs constant q Ri 10

q PROFILE

q PROFILE CLOSEUP

GROWTH RATES DRY vs MOIST for RiWARM CORE MOST UNSTABLE

Ri 40 qc 0.496 E vectors

Ri 100 WARM CORE MOST UNSTABLE

LARGE Ro X – Z CIRCULATION

y

x

z

WARM CORE CIRCULATION qc ~ 0.49 Ro ~ 0.9

P2

T

P1

C WC W

WARM CORE

CIRCULATION

WARM CORE WINDS LOWER

WARM CORE WINDS UPPER

WARM CORE PRESSURES 2D

WARM CORE THICKNESS 2D

WARM CORE PRESSURES 3D

WARM CORE THICKNESS 3D

PHASE DIFF P2 – P1

PHASE DIFF THK – W

QG DRY CASE q = 0

P1

T

P2

zy

x

QG CIRCULATION

C WC W

QG CIRCULATIO

N

DRY MOST UNSTABLELOWER WINDS

DRY MOST UNSTABLEUPPER WINDS

DRY MOST UNSTABLEPRESSURES 2D

DRY MOST UNSTABLETHICKNESS 2D

DRY MOST UNSTABLEPRESSURES 3D

DRY MOST UNSTABLETHICKNESS 3D

PHASE DIFF P2 – P1

PHASE DIFF THK – W

QG EADY Ri 10 DRY CASE q = 0

DRY EADY Ri 10LOWER WINDS

DRY EADY Ri 10UPPER WINDS

DRY EADY Ri 10PRESSURES 2D

DRY EADY Ri 10THICKNESS 2D

DRY EADY Ri 10PRESSURES 3D

DRY EADY Ri 10THICKNESS 3D

PHASE DIFF P2 – P1

PHASE DIFF THK – W

SUMMARY

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

WHAT’S NEXT?

• Make model non-frontal

• Add horizontal shear

• Nonlinear with random initial perturbation

ACKNOWLEDGMENT

Professor C. R. Mechosoand

Professor A. Arakawa

• Once a UCLA Atmos Science grad student

• Always a UCLA Atmos Science grad student

Ri 10 WARM CORE MOST UNSTABLE

WARM CORE WINDS LOWER

WARM CORE WINDS UPPER

WARM CORE PRESSURES 2D

WARM CORE PRESSURES 3D

WARM CORE THICKNESS 2D

WARM CORE THICKNESS 3D

W vs THICKNESS PHASE

W WARM CORE

W DRY CASE

W DRY EADY CASE

Ri 40 WARM CORE MOST UNSTABLE

WARM CORE WINDS LOWER

WARM CORE WINDS UPPER

WARM CORE PRESSURES 2D

WARM CORE PRESSURES 3D

WARM CORE THICKNESS 2D

WARM CORE THICKNESS 3D

Ri 1000 WARM CORE MOST UNSTABLE

WARM CORE WINDS LOWER

WARM CORE WINDS UPPER

WARM CORE PRESSURES 3D

WARM CORE PRESSURES 3D

WARM CORE THICKNESS 2D

WARM CORE THICKNESS 3D

MOST UNSTABLE q= 0.495 Ro = 1.52

QG DRY CASE PRESSURES 3DX – Z CROSS SECTION

QG DRY CASE THICKNESS 3DX – Z CROSS SECTION

MOST

UNSTABLE CIRUCLATIO

N q .495

P2

T

P1

C C W W

MOST UNSTABLE MODE CIRCULATION q = 0.495 Ro = 1.52

zy

x

MOST UNSTABLE WINDS LOWERq = 0.495

MOST UNSTABLE WINDS UPPERq = 0.495

MOST UNSTABLE PRESSURES 2Dq = 0.495

MOST UNSTABLE PRESSURES 3Dq = 0.495

MOST UNSTABLE THICKNESS 2Dq = 0.495

MOST UNSTABLE THICKNESS 3Dq = 0.495

MOST UNSTABLE PRESSURES q = 0.495 3D X – Z CROSS SECTION

MOST UNSTABLE THICKNESS q = 0.495 3D X – Z CROSS SECTION

CIRCULATION q = 0.495 Ro = 3.0

zy

x

P1

T

P2

w w c c

cc

HIGH Ro CIRCULATIO

N

NON DIM MOMENTUM EQN LARGE Ro CASE

Ro Ro

Ro