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 JPLJPL 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 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 OBSERVATION DETAILOBSERVATION DETAIL

POLAR LOW

THEORY

CISK FIGURE < 0 CISK C onditional I nstability of the S econd K ind 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 CAPE Ultra-violet catastrophe CISK CIFK

W ind I nduced S urface H eat E xchange WISHE > 0 WISHE FIGURE

WISHE Hypothesis 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 DETAILSHYPOTHESIS 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 core P2P2 T = P 2 – P 1 P1P1 C W AG GGEO vs AGEO TEMP ADV FOR WARM CORE z y x

MODEL

MODEL SCHEMATIC TWO LAYER SHALLOW WATER MODEL SCHEMATIC H1H1 H2H2 LxLx LyLy H WARM COLD

LINEARIZED MODEL EQUATIONS q q

LATENT HEAT SCHEMATICLATENT HEAT SCHEMATIC LATENT HEAT PARAMETERIZATION

-DIV -Q*DIV -(1-Q)DIV INITIAL Q = 0 AVG DENSITY INCREASES “COOLING” Q = 0.5 AVG DENSITY UNCHANGED “CONSTANT” DIV < 0 LATENT HEAT PARAMETERIZATION CASES Q > 0.5 AVG DENSITY DECREASES “WARMING”

ROSSBY NUMBERROSSBY NUMBER Ro

NON DIM MOMENTUM EQN Ro

MODEL ENERGETICS SCHEMATIC ZAPE EAPE W BC WQWQ EKE WKWK

MODEL ENERGETICS q

QG BAROCLINIC ENERGETICS q = 0 ZAPE EAPE W BC EKE WKWK Ro

QG SHORT WAVE CUTOFF q = 0 ZAPE EAPE W BC EKE WKWK Ro

CISK ENERGETICS q > 0.5 ZAPE EAPE W BC WQWQ EKE WKWK Ro

WISHE ENERGETICS q 0.5 ZAPE EAPE W BC WQWQ EKE WKWK Ro

Newton - Raphson confirms eigenvalues EIGENVALUE PROBLEM

PHASE LAGS T = P 2 – P 1 P2P2 P1P1 T 0° 90° 180° -90°

RESULTS

ENERGY VECTOR W BC G W BC AG -W BC G -W BC AG W BC > W Q W Q > W BC W BC AG W BC G

GROWTH RATES vs constant q Ri 10

q PROFILE

q PROFILE CLOSEUP

GROWTH RATES DRY vs MOIST for Ri WARM CORE MOST UNSTABLE

Ri 40 qc E vectors

Ri 100 WARM CORE MOST UNSTABLE

LARGE R o X – Z CIRCULATION y x z WARM CORE CIRCULATION qc ~ 0.49 R o ~ 0.9 P2P2 T P1P1 C W C W WARM CORE CIRCULATIONWARM 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

P1P1 T P2P2 z y x QG CIRCULATION C W C W QG CIRCULATIONQG CIRCULATION

DRY MOST UNSTABLE LOWER WINDS

DRY MOST UNSTABLE UPPER WINDS

DRY MOST UNSTABLE PRESSURES 2D

DRY MOST UNSTABLE THICKNESS 2D

DRY MOST UNSTABLE PRESSURES 3D

DRY MOST UNSTABLE THICKNESS 3D

PHASE DIFF P2 – P1

PHASE DIFF THK – W

QG EADY Ri 10 DRY CASE q = 0

DRY EADY Ri 10 LOWER WINDS

DRY EADY Ri 10 UPPER WINDS

DRY EADY Ri 10 PRESSURES 2D

DRY EADY Ri 10 THICKNESS 2D

DRY EADY Ri 10 PRESSURES 3D

DRY EADY Ri 10 THICKNESS 3D

PHASE DIFF P2 – P1

PHASE DIFF THK – W

SUMMARY

CONCLUSIONSCONCLUSIONS 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. Mechoso and 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 THICKNESS 2D

WARM CORE THICKNESS 3D

MOST UNSTABLE q= R o = 1.52

QG DRY CASE PRESSURES 3D X – Z CROSS SECTION

QG DRY CASE THICKNESS 3D X – Z CROSS SECTION

MOST UNSTABLE CIRUCLATION q.495MOST UNSTABLE CIRUCLATION q.495 P2P2 T P1P1 CC W W MOST UNSTABLE MODE CIRCULATION q = R o = 1.52 z y x

MOST UNSTABLE WINDS LOWER q = 0.495

MOST UNSTABLE WINDS UPPER q = 0.495

MOST UNSTABLE PRESSURES 2D q = 0.495

MOST UNSTABLE PRESSURES 3D q = 0.495

MOST UNSTABLE THICKNESS 2D q = 0.495

MOST UNSTABLE THICKNESS 3D q = 0.495

MOST UNSTABLE PRESSURES q = D X – Z CROSS SECTION

MOST UNSTABLE THICKNESS q = D X – Z CROSS SECTION

CIRCULATION q = R o = 3.0 z y x P1P1 T P2P2 wwcc cc HIGH Ro CIRCULATIONHIGH Ro CIRCULATION

NON DIM MOMENTUM EQN LARGE R o CASE RoRo RoRo RoRo