title sub synoptic scale instability and hurricane precursors doug sinton sjsu meteorology wednesday...
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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
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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
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OBSERVATIONS
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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
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POLAR LOW
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THEORY
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CISK FIGURE
< 0
CISK
Conditional Instability of the Second Kind
CAPE
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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
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Wind Induced Surface Heat Exchange
WISHE
> 0
WISHE FIGURE
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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
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TYPHOON SIZES
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HYPOTHESIS METHODOLOGY
LIMITATIONS
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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
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G vs AG TEMP ADV warm coreP2
T = P2 – P1
P1
C W
AGG GEO vs AGEO TEMP ADV FOR WARM CORE
zy
x
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MODEL
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MODEL SCHEMATICTWO LAYER SHALLOW WATER MODEL SCHEMATIC
H1
H2
Lx
Ly
H
WARM
COLD
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LINEARIZED MODEL EQUATIONS
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LATENT HEAT
SCHEMATIC
LATENT HEAT PARAMETERIZATION
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-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”
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ROSSBY NUMBER
Ro
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NON DIM MOMENTUM EQN
Ro Ro
Ro
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MODEL ENERGETICS SCHEMATIC
ZAPE
EAPE
WBC
WQ
EKEWK
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MODEL ENERGETICS
q
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QG BAROCLINIC ENERGETICS q = 0
ZAPE
EAPE
WBC
EKEWK
Ro
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QG SHORT WAVE CUTOFF q = 0
ZAPE
EAPE
WBC
EKEWK
Ro
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CISK ENERGETICS q > 0.5
ZAPE
EAPE
WBC
WQ
EKEWK
Ro
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WISHE ENERGETICS q 0.5
ZAPE
EAPE
WBC
WQ
EKEWK
Ro
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Newton - Raphson confirms eigenvalues
EIGENVALUE PROBLEM
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PHASE LAGS T = P2 – P1
P2
P1
T
0° 90°
180° -90°
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RESULTS
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ENERGY VECTOR
WBCGWBCAG
-WBCG
-WBCAG
WBC > WQ WQ > WBC
WBCAG
WBCG
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GROWTH RATES vs constant q Ri 10
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q PROFILE
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q PROFILE CLOSEUP
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GROWTH RATES DRY vs MOIST for RiWARM CORE MOST UNSTABLE
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Ri 40 qc 0.496 E vectors
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Ri 100 WARM CORE MOST UNSTABLE
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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
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WARM CORE WINDS LOWER
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WARM CORE WINDS UPPER
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WARM CORE PRESSURES 2D
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WARM CORE THICKNESS 2D
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WARM CORE PRESSURES 3D
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WARM CORE THICKNESS 3D
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PHASE DIFF P2 – P1
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PHASE DIFF THK – W
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QG DRY CASE q = 0
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P1
T
P2
zy
x
QG CIRCULATION
C WC W
QG CIRCULATIO
N
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DRY MOST UNSTABLELOWER WINDS
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DRY MOST UNSTABLEUPPER WINDS
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DRY MOST UNSTABLEPRESSURES 2D
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DRY MOST UNSTABLETHICKNESS 2D
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DRY MOST UNSTABLEPRESSURES 3D
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DRY MOST UNSTABLETHICKNESS 3D
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PHASE DIFF P2 – P1
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PHASE DIFF THK – W
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QG EADY Ri 10 DRY CASE q = 0
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DRY EADY Ri 10LOWER WINDS
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DRY EADY Ri 10UPPER WINDS
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DRY EADY Ri 10PRESSURES 2D
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DRY EADY Ri 10THICKNESS 2D
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DRY EADY Ri 10PRESSURES 3D
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DRY EADY Ri 10THICKNESS 3D
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PHASE DIFF P2 – P1
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PHASE DIFF THK – W
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SUMMARY
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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
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WHAT’S NEXT?
• Make model non-frontal
• Add horizontal shear
• Nonlinear with random initial perturbation
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ACKNOWLEDGMENT
Professor C. R. Mechosoand
Professor A. Arakawa
• Once a UCLA Atmos Science grad student
• Always a UCLA Atmos Science grad student
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Ri 10 WARM CORE MOST UNSTABLE
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WARM CORE WINDS LOWER
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WARM CORE WINDS UPPER
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WARM CORE PRESSURES 2D
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WARM CORE PRESSURES 3D
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WARM CORE THICKNESS 2D
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WARM CORE THICKNESS 3D
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W vs THICKNESS PHASE
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W WARM CORE
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W DRY CASE
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W DRY EADY CASE
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Ri 40 WARM CORE MOST UNSTABLE
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WARM CORE WINDS LOWER
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WARM CORE WINDS UPPER
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WARM CORE PRESSURES 2D
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WARM CORE PRESSURES 3D
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WARM CORE THICKNESS 2D
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WARM CORE THICKNESS 3D
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Ri 1000 WARM CORE MOST UNSTABLE
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WARM CORE WINDS LOWER
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WARM CORE WINDS UPPER
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WARM CORE PRESSURES 3D
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WARM CORE PRESSURES 3D
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WARM CORE THICKNESS 2D
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WARM CORE THICKNESS 3D
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MOST UNSTABLE q= 0.495 Ro = 1.52
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QG DRY CASE PRESSURES 3DX – Z CROSS SECTION
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QG DRY CASE THICKNESS 3DX – Z CROSS SECTION
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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
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MOST UNSTABLE WINDS LOWERq = 0.495
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MOST UNSTABLE WINDS UPPERq = 0.495
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MOST UNSTABLE PRESSURES 2Dq = 0.495
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MOST UNSTABLE PRESSURES 3Dq = 0.495
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MOST UNSTABLE THICKNESS 2Dq = 0.495
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MOST UNSTABLE THICKNESS 3Dq = 0.495
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MOST UNSTABLE PRESSURES q = 0.495 3D X – Z CROSS SECTION
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MOST UNSTABLE THICKNESS q = 0.495 3D X – Z CROSS SECTION
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CIRCULATION q = 0.495 Ro = 3.0
zy
x
P1
T
P2
w w c c
cc
HIGH Ro CIRCULATIO
N
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NON DIM MOMENTUM EQN LARGE Ro CASE
Ro Ro
Ro