Diabatic Processes Diabatic processes are non-adiabatic processes such as precipitation fall-out entrainment and mixing radiative heating or cooling
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.
Microphysics water vapor condensation evaporation cloud droplets (Er) evaporation (C) condensation collection (Ar) rain drops (Pr) fall out (precipitation)
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 =2 10 2 mb 1.
Entrainment Entrainment is the incorporation of environmental air into a parcel or cloud.
2.5 Evidence for Entrainment in Cu Liquid water content (g m 3 ) 2.0 1.5 1.0 0.5 Adiabatic LWC 0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Distance (km)
Evidence for Entrainment in Cu 2500 Adiabatic LWC Height above cloud base (m) 2000 1500 1000 500 0 0 1 2 Liquid water content, LWC (g m 3 ) 3 4 5
Entrainment in Stratocumulus
Entrainment in Stratocumulus Entrainment in a 1500 a) e) 3D high-resolution simulation of Sc. Altitude (m) 1250 1000 1500 b) f) Altitude (m) 1250 1000 1500 c) g) Altitude (m) 1250 1000 1500 d) h) Altitude (m) 1250 1000 1500 2000 2500 3000 1500 2000 2500 3000 Horizontal distance Horizontal distance
Entrainment: Kelvin-Helmholtz Instability
Entrainment into a turbulent jet
droplet evaporation molecular diffusion turbulent deformation entrainment saturated parcel
Fractional Rate of Entrainment 8.33 g/kg (10 100 + 0 20)/(100 + 20) = 8.33 120 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
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.
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 ).
Entrainment ˆD θ = λ(θ θ e ), ˆD w = λ(w w e ), ˆD l = λ(l l e )= λl.
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.
Entrainment pressure (mb) 800 850 900 lem50 lem100 lem200 entrainment only λ =1.5 km 1 950 0.0 0.2 0.4 0.6 0.8 1.0 Fraction of unmixed cloud base air