Diabatic Processes. Diabatic processes are non-adiabatic processes such as. entrainment and mixing. radiative heating or cooling

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1 Diabatic Processes Diabatic processes are non-adiabatic processes such as precipitation fall-out entrainment and mixing radiative heating or cooling

2 Parcel Model dθ dt dw dt dl dt dr dt = L c p π (C E r)+d θ = (C E r )+D w = C A r + D l = P r + A r E r + D r π =( p/p 0 ) R/c p, C is the net condensation rate, E r is the rain evaporation rate, A r is the cloud-to-rain water conversion rate, P r is the convergence of rain water flux, and D i represents the effects of entrainment and mixing.

3 Microphysics water vapor condensation evaporation cloud droplets (Er) evaporation (C) condensation collection (Ar) rain drops (Pr) fall out (precipitation)

4 Diabatic Processes A r Process rates per unit time interval: dl dt conversion to rain = dr dt conversion from cloud water Process rates per unit pressure interval: dl dp = Ĉ Âr + ˆD l Âr dl dp conversion to rain = Cl, for dp/dt < 0 only, with C = mb 1.

5 Entrainment Entrainment is the incorporation of environmental air into a parcel or cloud.

6 2.5 Evidence for Entrainment in Cu Liquid water content (g m 3 ) Adiabatic LWC Distance (km)

7 Evidence for Entrainment in Cu 2500 Adiabatic LWC Height above cloud base (m) Liquid water content, LWC (g m 3 ) 3 4 5

8 Entrainment in Stratocumulus

9 Entrainment in Stratocumulus Entrainment in a 1500 a) e) 3D high-resolution simulation of Sc. Altitude (m) b) f) Altitude (m) c) g) Altitude (m) d) h) Altitude (m) Horizontal distance Horizontal distance

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11 Entrainment: Kelvin-Helmholtz Instability

12 Entrainment into a turbulent jet

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15 droplet evaporation molecular diffusion turbulent deformation entrainment saturated parcel

16 Fractional Rate of Entrainment 8.33 g/kg ( )/( ) = kg mixing 8.33 g/kg 10 g/kg 0 g/kg 120 kg entrainment 20 kg 10 g/kg mixing ratio 10 g/kg 100 kg mass

17 Entrainment The fractional rate of entrainment of a parcel of mass m that entrains a blob of mass dm while the pressure changes by dp (due to ascent) is ˆλ 1 m dm dp. The rate of change of a scalar φ due to entrainment is ˆD φ dφ dp entrainment = ˆλ(φ φ e ), where φ e is the value of φ in the entrained air.

18 Entrainment We can derive this from dφ dp entrainment = lim p 0 φ after ent φ before ent p using φ before ent = φ and Substitution gives dφ dp entrainment φ after ent = mφ + m φ e m + m. = lim p 0 = 1 m dm 1 m + m m p (φ φ e) dp (φ φ e)= ˆλ(φ φ e ).

19 Entrainment ˆD θ = λ(θ θ e ), ˆD w = λ(w w e ), ˆD l = λ(l l e )= λl.

20 Entrainment In cumulus clouds, the fractional rate of entrainment, λ (1/m) dm/dz, ranges from about 0.1 km 1 to 2 km 1. Cloud-top height is largely determined by λ: deep clouds are associated with small values, and shallow clouds with large values. Field studies suggest that λ 0.2/R, where R is the cloud radius.

21 Entrainment pressure (mb) lem50 lem100 lem200 entrainment only λ =1.5 km Fraction of unmixed cloud base air