1. Cumulus Clouds

2. Instabilities Resulting in Vertical Overturning 1.Thermal Instability (Assuming uniform vertical pressure gradient) a) Static (Parcel buoyancy) b) Conditional (Parcel buoyancy) c) Rayleigh Benard (Parcel buoyancy, surface friction) 2.Dynamic Instabilities a) Shear (or inflection point) (Vorticity or shear gradient) (analogous to barotropic instability) 3. Dynamic-Thermal Instabilities a) Vertical Shear vs Static Stability i. Kelvin-Helmholtz iii Gravity wave [convection (growing), evanecent (decaying)] b) Inertial production (Horizontal Shear) vs Static Stability i. Symmetric Instability ii. Conditional Symmetric Instability (CSI) ii Convective - Symmetric Instability(C-SI)

3. General Classification of Moist Convection Shallow Cumulus (cumulus, scatted cumulus, strato-cumulus) –Depth small compared to scale height of troposphere, i.e. –Usually confined to Planetary Boundary Layer (PBL) –Typically non-precipitating –Surface friction plays critical role to organization Deep Cumulus (congestus, cumulonimbi) –Depth comparable to scale height of troposphere –Precipitating –Friction plays secondary role to organization

4. What goes on inside a cumulus cloud?

5. Evolution of a thermal from a Numerical Model

6. Conceptual Model Series of convective plumes rising to form individual turrets comprising cloud Each rising pulse a toroidal circulation Successive toroids give rise to mean upward current called updraft Sustained downward current between toroids, if existing, would be downdraft

8. Liquid Water Content

9. What causes liquid water content to be below adiabatic LWC? Lateral entrainment –Neutral mixing –Dynamic entrainment Cloud Top Entrainment

10. Bubble and Jet Models of Convection <= mixing lateral entrainment

11. Dynamic Lateral Entrainment

12. Dynamic Entrainment

13. Effects of Dynamic Lateral Entrainment

15. Cloud Top entrainment

16. Deep Cumulus Must consider impact of precipitation on cumulus circulation Must consider pressure effects because of cloud depth –Thermodynamic pressure, ie hydrostatic pressure –Dynamic pressure due to inertia of air motions Friction layer small compared to cloud and we generally ignore friction

17. Vertical Acceleration (using Pressure) Inertia Pressure Buoyancy

18. Vertical Acceleration (Using Total Pressure) Inertia Pressure Buoyancy

19. Vertical Acceleration (using Exner function) Inertia Pressure Buoyancy

20. Traditional Buoyancy |||| Warm/Cold air rises/sinks Vapor less dense than dry air Liquid water loading Ice water loading

21. Anelastic Approximation Neglect frequencies higher than those associated with meteorological phenomena such as sound wave frequencies Similar to incompressible assumption, but for a compressible system

22. Continuity Equation

23. Multiply momentum equation (momentum form) by density:

24. Multiply momentum equation (vorticity form) by density:

25. Decomposition of Pressure into Dynamic and Buoyancy Pressure

26. Dynamics (or inertia) Terms

27. Buoyancy Terms

28. Take divergence of density multiplied by three momentum equations and then result set to zero and solve for pressure: or Where pressure is divided into dynamic and buoyancy pressure contributions

29. Buoyancy vs. Dynamic Pressure Dynamic pressure,, is zero if flow is at rest. Buoyancy pressure,, is hydrostatic pressure for flow at rest. Dynamic pressure results from inertia such as: –Rotation (cyclostrophic pressure) –Straight line accelerations –Coordinate system accelerations (coriolis) Buoyancy pressure results from: –Moisture anomalies –Thermal anomalies –Condensate (precipitation drag)

30. Real Buoyancy Acceleration True buoyancy acceleration is : Where we see the acceleration is caused by thermal, moisture or precipitation drag anomalies

31. Dynamic Pressure Acceleratrion True dynamic pressure gradient acceleration is : Where we see the acceleration is caused by inertial effects of rotation, straight line movement and coordinate system movement

32. Conditional Instability of the First Kind Occurs when a parcel is statically unstable when saturated but stable when dry Results in the formation of moist convective thermal plumes, ie cumulus clouds Instability favors horizontal scales ~ vertical scale of overturning, i.e. meso-gamma scale for deep convection

33. Three Stages of a Deep Convective Thermal Simplest Case: –Conditionally unstable for deep convection –No environmental wind –Dry middle layers –Moist unstable boundary layer

34. Stage 1 : Cumulus Stage Updraft only Cloud droplets only (no precipitation) Level of Non-divergence (LND) near top of moist Planetary Boundary Layer (PBL) Cloud positively buoyant throughout: Environment neutrally buoyant Low pressure under updraft High pressure throughout cloud

36. Stage 2 : Mature Stage Updraft and downdraft Precipitation and cloud droplets throughout cloud Level of Non-divergence (LND) at middle levels Cloud positively buoyant at middle levels, negatively buoyant in lower part Cold air dome (density current) at surface Environment neutrally buoyant but warming Low pressure at middle levels High pressure at surface and top of cloud

38. Stage 3 : Dissipating Stage Downdraft only Precipitation only throughout cloud Level of Non-divergence (LND) at upper levels Cloud negatively buoyant throughout Environment positively buoyant Low pressure at middle levels and above in cloud High pressure at surface Low pressure at surface of environment

40. Reasons for Breakdown Water loading of updraft from precipitation drag Cooling due to dynamic entrainment of mid level dry air

41. Introduce Environmental Wind Shear to Prevent Breakdown Assume: –two-dimensions, i.e. infinitely long convective line –Straight-line shear with height, I.e. wind speed change with without direction change

43. Three-Dimensional Effect of Wind Shear As before but now assume convective plume is initially circular rather than infinitely long Also start by assuming a straight line shear profile again Assume westerly shear and veering winds in lowest 6 km

44. View from South

45. View from East

46. Helicity

47. Convective Richardson Number

48. CAPE

49. Wind Shear