1. Copyright © 2009 R. R. Dickerson & Z.Q. Li 1 Convection: Parcel Theory Chapt. 4 page 48. Vertical motion of parcels of air. Buoyant convection leads to the formation of cumulus clouds (though other clouds have convective features). Parcel theory is an elementary treatment, but useful for qualitative understanding.

2. Copyright © 2009 R. R. Dickerson & Z.Q. Li 2 Parcel Theory Assumptions Parcel and environment are in dynamic equilibrium: P = P’. Parcel maintains its identity; no mixing with environment. Atmosphere in hydrostatic equilibrium. No compensating motion by atmosphere as parcel moves.

3. Copyright © 2009 R. R. Dickerson & Z.Q. Li 3 Parcel theory equations: Primes: environmental properties. You can correct for the effect of moisture on density by using virtual temperature wherever T appears here. Let B be buoyancy. or with

4. Copyright © 2009 R. R. Dickerson & Z.Q. Li 4 Designate updraft velocity then so and

5. Copyright © 2009 R. R. Dickerson & Z.Q. Li 5 Alternate formulation using >>  = P’/R’T’ and dP’ = -  gdz

6. Copyright © 2009 R. R. Dickerson & Z.Q. Li 6 T -RlnP T’ Parcel process curve (environment) Hatched area is proportional to the kinetic energy of the parcel. Change in area from level to level represents the change in K.E.

7. Copyright © 2009 R. R. Dickerson & Z.Q. Li 7 Correcting for Condensed H 2 O Let

8. Copyright © 2009 R. R. Dickerson & Z.Q. Li 8 Parcel Theory is Useful for: Estimating cloud base and top heights Estimating stability Estimating vertical motion U But we’ve neglected Drag Mixing Compensating motion by environment Effects of condensed water Therefore: parcel theory U => expected upper limit.