Convection Parcel Theory RY Chapt 4 page 48
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Convection: Parcel Theory R&Y Chapt. 4 page 48; Salby Chapt. 7; W&H Chapt 8. • 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. Copyright © 2017 R. R. Dickerson & Z. Q. Li 1
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. Copyright © 2009 R. R. Dickerson & Z. Q. Li 2
Parcel theory equations: or 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. with Copyright © 2009 R. R. Dickerson & Z. Q. Li 3
Designate updraft velocity then so and Copyright © 2009 R. R. Dickerson & Z. Q. Li 4
Alternate formulation using >> r = P’/R’T’ and d. P’ = - rgdz Copyright © 2009 R. R. Dickerson & Z. Q. Li 5
T’ (environment) -Rln. P Parcel process curve T Hatched area is proportional to the kinetic energy of the parcel. Change in area from level to level represents the change in K. E. Check units: area integral of Rln. P wrt T R = J kg-1 K-1 and area = J/kg. Copyright © 2009 R. R. Dickerson & Z. Q. Li 6
Correcting for Condensed H 2 O Let Copyright © 2009 R. R. Dickerson & Z. Q. Li 7
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. Copyright theory U => expected upper limit. 8 © 2009 R. R. Dickerson & Z. Q. Li
