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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




Cisk figure

ConditionalInstabilityof theSecondKind

CISK FIGURE

CISK

< 0

CAPE


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 figure

WindInducedSurfaceHeat Exchange

WISHE FIGURE

WISHE

> 0


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 methodology limitations
HYPOTHESISMETHODOLOGYLIMITATIONS


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



Model schematic

TWO LAYER SHALLOW WATER MODEL SCHEMATIC

MODEL SCHEMATIC

COLD

H

H2

H1

Ly

WARM

Lx



Latent heat schematic

LATENT HEAT PARAMETERIZATION

LATENT HEAT SCHEMATIC


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


R o s s b y n u m b e r
ROSSBYNUMBER

Ro



Model energetics schematic
MODEL ENERGETICS SCHEMATIC

ZAPE

WBC

WK

EAPE

EKE

WQ



Qg baroclinic energetics q 0
QGBAROCLINIC ENERGETICSq = 0

ZAPE

WBC

WK

EAPE

EKE

Ro


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


Growth rates vs constant q ri 10
GROWTH RATES vs constantq Ri10


Q profile
qPROFILE


Q profile closeup
qPROFILE CLOSEUP


Growth rates dry vs moist for ri warm core most unstable
GROWTH RATESDRY vs MOIST for RiWARM CORE MOST UNSTABLE


Ri 40 qc 0 496 e vectors
Ri 40 qc0.496 E vectors


Ri 100 warm core most unstable
Ri 100WARM COREMOST UNSTABLE


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


Warm core winds lower
WARM CORE WINDSLOWER



Warm core pressures 2d
WARM CORE PRESSURES2D


Warm core thickness 2d
WARM CORE THICKNESS2D


Warm core pressures 3d
WARM CORE PRESSURES3D


Warm core thickness 3d
WARM CORE THICKNESS3D


Phase diff p2 p1
PHASE DIFFP2–P1


Phase diff thk w
PHASE DIFFTHK – W


Qg dry case q 0
QGDRY CASE q = 0


Qg circulation

QGCIRCULATION

QG CIRCULATION

P2

T

C

C

W

W

P1

z

y

x


Dry most unstable lower winds
DRY MOST UNSTABLELOWER WINDS


Dry most unstable upper winds
DRY MOST UNSTABLEUPPERWINDS


Dry most unstable pressures 2d
DRY MOST UNSTABLEPRESSURES2D


Dry most unstable thickness 2d
DRY MOST UNSTABLETHICKNESS2D


Dry most unstable pressures 3d
DRY MOST UNSTABLEPRESSURES3D


Dry most unstable thickness 3d
DRY MOST UNSTABLETHICKNESS3D


Phase diff p2 p11
PHASE DIFFP2–P1


Phase diff thk w1
PHASE DIFFTHK – W


Qg eady ri 10 dry case q 0
QG EADY Ri 10DRY CASE q = 0


Dry eady ri 10 lower winds
DRY EADY Ri 10LOWER WINDS


Dry eady ri 10 upper winds
DRY EADY Ri 10UPPERWINDS


Dry eady ri 10 pressures 2d
DRY EADY Ri 10PRESSURES2D


Dry eady ri 10 thickness 2d
DRY EADY Ri 10THICKNESS2D


Dry eady ri 10 pressures 3d
DRY EADY Ri 10PRESSURES3D


Dry eady ri 10 thickness 3d
DRY EADY Ri 10THICKNESS3D


Phase diff p2 p12
PHASE DIFFP2–P1


Phase diff thk w2
PHASE DIFFTHK – W



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


Ri 10 warm core most unstable
Ri 10 WARM COREMOST UNSTABLE


Warm core winds lower1
WARM CORE WINDSLOWER



Warm core pressures 2d1
WARM CORE PRESSURES2D


Warm core pressures 3d1
WARM CORE PRESSURES3D


Warm core thickness 2d1
WARM CORE THICKNESS2D


Warm core thickness 3d1
WARM CORE THICKNESS3D



W warm core
W WARM CORE


W dry case
W DRY CASE


W dry eady case
W DRY EADY CASE


Ri 40 warm core most unstable
Ri 40WARM COREMOST UNSTABLE


Warm core winds lower2
WARM CORE WINDSLOWER



Warm core pressures 2d2
WARM CORE PRESSURES2D


Warm core pressures 3d2
WARM CORE PRESSURES3D


Warm core thickness 2d2
WARM CORE THICKNESS2D


Warm core thickness 3d2
WARM CORE THICKNESS3D


Ri 1000 warm core most unstable
Ri 1000WARM COREMOST UNSTABLE


Warm core winds lower3
WARM CORE WINDSLOWER



Warm core pressures 3d3
WARM CORE PRESSURES3D


Warm core pressures 3d4
WARM CORE PRESSURES3D


Warm core thickness 2d3
WARM CORE THICKNESS2D


Warm core thickness 3d3
WARM CORE THICKNESS3D


Most unstable q 0 495 r o 1 52
MOST UNSTABLE q= 0.495 Ro = 1.52


Qg dry case pressures 3d x z cross section
QGDRY CASEPRESSURES3DX – Z CROSS SECTION


Qg dry case thickness 3d x z cross section
QGDRY CASETHICKNESS 3DX – Z CROSS SECTION


Most unstable ciruclation q 495

MOST UNSTABLE MODE CIRCULATION q = 0.495Ro = 1.52

MOST UNSTABLE CIRUCLATION q .495

P2

C

C

W

W

T

P1

z

y

x


Most unstable winds lower q 0 495
MOST UNSTABLEWINDSLOWERq = 0.495


Most unstable winds upper q 0 495
MOST UNSTABLEWINDSUPPERq = 0.495


Most unstable p ressures 2d q 0 495
MOST UNSTABLE PRESSURES2Dq = 0.495


Most unstable p ressures 3d q 0 495
MOST UNSTABLE PRESSURES3Dq = 0.495


Most unstable thickness 2d q 0 495
MOST UNSTABLE THICKNESS 2Dq = 0.495


Most unstable thickness 3d q 0 495
MOST UNSTABLE THICKNESS 3Dq = 0.495


Most unstable pressures q 0 495 3d x z cross section
MOSTUNSTABLEPRESSURESq = 0.495 3DX – Z CROSS SECTION


Most unstable thickness q 0 495 3d x z cross section
MOSTUNSTABLETHICKNESSq = 0.495 3DX – Z CROSS SECTION


High ro circulation

CIRCULATIONq= 0.495 Ro = 3.0

HIGH Ro CIRCULATION

P2

w

w

c

c

T

c

c

P1

z

y

x



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