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

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

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

Example Skew-T Diagrams 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) Deep lifting required LIttle lifting required

Homework 1.3a Density Current Theoretical speed of propagation: 

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

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

Severe Weather Forecasting

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

"Low-level Jet"

Bluestein Volume II (282) Source: Bluestein (1993)

Severe Weather Composites

Bluestein (1993) Bluestein Volume II (440)

Sounding Types:

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) Deep lifting required LIttle lifting required

Bluestein Volume II (450) Source: Bluestein (1993)

Bluestein Volume II (452) Source: Bluestein (1993)

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

Sounding Evolution!!!!!!!!!!

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

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

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

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

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

Moisture Tendency Equation mean advection eddy flux convergence diabatic sources