1. anelastic: Boussinesque: Homework 1.1 …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. 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

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

9. Severe Weather Forecasting

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

17. "Low-level Jet"

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

25. Severe Weather Composites

26. Bluestein (1993)
Bluestein Volume II
(440)

27. Sounding Types:

28. 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

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

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

31. 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

33. Sounding Evolution!!!!!!!!!!

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

36. 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

37. 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

38. 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

41. 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)

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