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Homework Assignments for Atmospheric Science Course

This collection of homework assignments covers topics such as anelasticity, Boussinesq approximation, CAPE, Skew-T Diagrams, density currents, severe weather forecasting, and turbulent heat and moisture fluxes.

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Homework Assignments for Atmospheric Science Course

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  1. Homework 1.1 anelastic: …eliminates sound waves …eliminates prognostic P Boussinesque: …shallow flow …density perturbations are small but... retained

  2. Homework 1.2b Assume steady state, p’ small, u,v =0…

  3. Homework 1.2a CAPE=1000 j/kg Wmax=45 ms-1 CAPE=5000 j/kg Wmax=100 ms-1 Qr = 10 g/kg over 6 km Q-CAPE = 1200 j/kg

  4. Homework 1.2b Example Skew-T Diagrams Central U.S. Warm-Season Oceanic Tropical • Characteristics (CAPE=2750 J/kg, CIN=110 J/Kg): • Moderate PBL RH • Stable layer above PBL • Steep midtropospheric lapse rate (very unstable) • Characteristics (CAPE=1000 J/kg, CIN=10 J/Kg): • High PBL RH • No stable layer above PBL • Nearly moist-neutral lapse rate (slightly unstable) LIttle lifting required Deep lifting required

  5. Homework 1.3a Density Current Theoretical speed of propagation: 

  6. Homework 1.3a 2 hPa -4 K 1500 m 20 ms-1

  7. Homework 1.3b DCAPE Potentially coldest air in a cold pool descends from the level of minimum ThetaE

  8. Severe Weather Forecasting

  9. Severe Weather Forecasting S S T …Stability …Shear …Trigger

  10. "Low-level Jet"

  11. Source: Bluestein (1993)

  12. Severe Weather Composites

  13. Bluestein (1993)

  14. Sounding Types:

  15. Example Skew-T Diagrams Central U.S. Warm-Season Oceanic Tropical • Characteristics (CAPE=2750 J/kg, CIN=110 J/Kg): • Moderate PBL RH • Stable layer above PBL • Steep midtropospheric lapse rate (very unstable) • Characteristics (CAPE=1000 J/kg, CIN=10 J/Kg): • High PBL RH • No stable layer above PBL • Nearly moist-neutral lapse rate (slightly unstable) LIttle lifting required Deep lifting required

  16. Source: Bluestein (1993)

  17. Source: Bluestein (1993)

  18. Some Other Examples Western U.S. Warm Season Central U.S. “Elevated” Instability • Deep, dry PBL with moist midlevels • Strong downdraft, wind potential, little rain • Most unstable air with little CIN located above PBL • Common at night and north of warm/stationary fronts

  19. Sounding Evolution!!!!!!!!!!

  20. Lapse Rate Tendency Equation differential horizontal advection differential vertical motion differential diabatic forcing

  21. Turbulent Heat and Moisture Fluxes • PBL growth depends on several • factors including: • vigor of turbulent eddies • stability of air above PBL Daytime heating results in increase of PBL depth and potential temperature

  22. Turbulent Heat and Moisture Fluxes (Cont.) • In quiescent conditions the vertical moisture flux convergence < 0 • term can be critical • Unlike q, qv decreases above PBL • When not balanced by surface • evaporation or moisture advection, • as PBL grows qv can decrease • significantly due to vertical flux term • Large temporal decreases most • common when dry air exists above • PBL and inversion is not too strong In this example vertical heat flux convergence > 0 in PBL helps eliminate CIN but the strong drying from vertical moisture flux reduces PBL CAPE

  23. Turbulent Heat and Moisture Fluxes (Cont.) • Different Example (Day Before, Same Location and Quiescent Synoptic Condition) • Stronger initial inversion and moister • conditions above the PBL than • previous example • No temporal drop in PBL qv In this example, the heating/vertical mixing process also reduces CIN but this time results in increased PBL CAPE

  24. Effects of Layer Lifting on Potentially Unstable Sounding • Initial Sounding: • No CAPE for any parcels • Final Sounding: • Deep Moist Absolutely • Unstable Layer (MAUL) • Positive CAPE w/ no CIN Layer Lifting From Bryan and Fritsch (2000, BAMS)

  25. Moisture Tendency Equation mean advection eddy flux convergence diabatic sources

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