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  1. 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

  2. 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

  3. OBSERVATIONS

  4. 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

  5. POLAR LOW

  6. THEORY

  7. ConditionalInstabilityof theSecondKind CISK FIGURE CISK < 0 CAPE

  8. 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

  9. WindInducedSurfaceHeat Exchange WISHE FIGURE WISHE > 0

  10. 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

  11. TYPHOON SIZES

  12. HYPOTHESISMETHODOLOGYLIMITATIONS

  13. 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

  14. G GEOvsAGEOTEMPADV FORWARMCORE G vs AG TEMP ADV warm core AG P2 C T =P2–P1 W P1 z y x

  15. MODEL

  16. TWO LAYER SHALLOW WATER MODEL SCHEMATIC MODEL SCHEMATIC COLD H H2 H1 Ly WARM Lx

  17. LINEARIZED MODEL EQUATIONS q q

  18. LATENT HEAT PARAMETERIZATION LATENT HEAT SCHEMATIC

  19. 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

  20. ROSSBYNUMBER Ro

  21. NON DIM MOMENTUM EQN Ro Ro Ro

  22. MODEL ENERGETICS SCHEMATIC ZAPE WBC WK EAPE EKE WQ

  23. MODEL ENERGETICS q

  24. QGBAROCLINIC ENERGETICSq = 0 ZAPE WBC WK EAPE EKE Ro

  25. QGSHORT WAVE CUTOFFq = 0 ZAPE WBC WK EAPE EKE Ro

  26. CISK ENERGETICSq > 0.5 ZAPE WBC WK EAPE EKE Ro WQ

  27. WISHE ENERGETICSq0.5 ZAPE WBC WK EAPE EKE WQ Ro

  28. EIGENVALUE PROBLEM Newton - Raphson confirms eigenvalues

  29. P2 PHASE LAGS T=P2–P1 T P1 0° 90° 180° -90°

  30. RESULTS

  31. ENERGY VECTOR WBCG WBCAG -WBCG WBCAG -WBCAG WBCG WBC > WQ WQ > WBC

  32. GROWTH RATES vs constantq Ri10

  33. qPROFILE

  34. qPROFILE CLOSEUP

  35. GROWTH RATESDRY vs MOIST for RiWARM CORE MOST UNSTABLE

  36. Ri 40 qc0.496 E vectors

  37. Ri 100WARM COREMOST UNSTABLE

  38. WARMCORECIRCULATIONqc ~ 0.49 Ro ~ 0.9 WARM CORE CIRCULATION LARGE Ro X – Z CIRCULATION P2 C C W W T P1 z y x

  39. WARM CORE WINDSLOWER

  40. WARM CORE WINDS UPPER

  41. WARM CORE PRESSURES2D

  42. WARM CORE THICKNESS2D

  43. WARM CORE PRESSURES3D

  44. WARM CORE THICKNESS3D

  45. PHASE DIFFP2–P1

  46. PHASE DIFFTHK – W

  47. QGDRY CASE q = 0

  48. QGCIRCULATION QG CIRCULATION P2 T C C W W P1 z y x

  49. DRY MOST UNSTABLELOWER WINDS

  50. DRY MOST UNSTABLEUPPERWINDS