Droplet stochastic activation and spectrum broadening in the - - PowerPoint PPT Presentation

Droplet stochastic activation and spectrum broadening

in the presence of supersaturation fluctuations

Gustavo C. Abade1, W. W. Grabowski2, H. Paw lowska1

1University of Warsaw, Faculty of Physics, Institute of Geophysics, Warsaw,

Poland

2National Center for Atmospheric Research, Boulder, USA

July 9, 2018

LES of cloud-scale flow

cloud updraft and interfacial instabilities (entraiment)

Lasher-Trapp et al., QJRMS, 131 (2005)

Microphysics

Droplet growth dr dt = 1 r D S Mean-field supersaturation S = e es − 1 LES grid box

∆ ∆

water droplet moist air

r ∆ ∼ tens of meters (inertial range)

Microphysical variability

at sub-grid scales (SGS)

◮ S = S + S′ ◮ Entrainment of

unsaturated air + CCN

◮ SGS mixing ◮ Activation/deactivation ◮ Lagrangian method

Entraiment Entraiment CCN

Stochastic growth

K¨

• hler curve and potential

rdr dt = D

• S−A

r + B r3

• x ≡ r2

S = S + S′ dx dt = −∂V ∂x + 2DS′

Sc Koehler curve unstable stable Seq(r) rd rc 0.1 1 10 〈S〉 < Sc 〈S〉 = Sc 〈S〉 > Sc Koehler potential V(r) r [µm]

Stochastic activation and growth

driven by supersaturation fluctuations rdr dt = D

• S−A

r + B r3

• x ≡ r2

S = S + S′ dx dt = −∂V ∂x + 2DS′

Sc Seq(r) rd r1 rc r2 0 < 〈S〉 < Sc V〈S〉(r) r

cloud haze droplet droplet SDA SA

Stochastic activation (SA) / deactivation (SDA)

Supersaturation and velocity fluctuations

W W ′

i

Si

T and p decreasing

dS′

i

dt = −S′

i

τc − S′

i

τm + aW ′

i(t)

τc ∼ 1 DNr (condensation) τm ∼ eddy turnover time (mixing)

◮ Statistics of W ′(t)?

Grabowski and Abade, JAS, 74 (2017)

Entraining cloud parcel

stochastic entrainment events

λ ∼ 200 m µ = 1 m dm dt W

cooler cool warm

decreasing pressure unsaturated air entraiment of + CCN entrainment rate and temperature LCL Krueger et al., JAS, 54 (1997); Romps and Kuang, JAS, 67 (2010)

Droplet-size distribution

after a 1-km parcel rise

0.05 0.1 0.15 0.2 0.25 0.3 8.8 PDF(r > rc) (µm-1) (a) adiabatic, non-turbulent adiabatic, turbulent entraining, non-turbulent entraining, turbulent 0.01 0.1 1 5 10 15 20 25 PDF(r) (µm-1) r (µm) (b)

Stochastic CCN activation

adiabatic parcel

Stochastic CCN activation

• 1
• 0.5

0.5 1 〈S〉 (%) (a) adiabatic non-turbulent adiabatic turbulent

• 1
• 0.5

0.5 1 0.2 0.4 0.6 0.8 1 50 100 150 200 Nc / NCCN t [s] (b) 0.2 0.4 0.6 0.8 1 50 100 150 200

• 1
• 0.5

0.5 1 〈S〉 (%) (c) entraining non-turbulent entraining turbulent

• 1
• 0.5

0.5 1 50 100 150 200 0.2 0.4 0.6 0.8 1 Nc / NCCN t [s] (d) 50 100 150 200 0.2 0.4 0.6 0.8 1

Entraining parcel Adiabatic parcel

2-D kinematic simulations

0.3 0.6 0.9 1.2 1.5 0.3 0.6 0.9 1.2 1.5 LCL z (km) x (km)

◮ Prescribed flow u(r) ◮ Balance equations for entropy

and water vapor

◮ Super-droplets ◮ ǫ = 10−3 m2 s−3 everywhere

2-D kinematic simulations

0.3 0.6 0.9 1.2 1.5 0.3 0.6 0.9 1.2 1.5 LCL z (km) x (km)

◮ Prescribed flow u(r) ◮ Balance equations for entropy

and water vapor

◮ Super-droplets ◮ ǫ = 10−3 m2 s−3 everywhere

2-D kinematic simulations

Droplet-size PDF

0.3 0.6 0.9 1.2 1.5 0.3 0.6 0.9 1.2 1.5 z (km) x (km) 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Liquid-water mixing ratio (g/kg) 0.2 0.4 0.6 0.8 1 1.2 1.4 (a) z = 1.4 km non-turbulent ε = 10-3 m2 s-3 0.2 0.4 0.6 0.8 1 1.2 PDF(r) [µm-1] (b) z = 1.2 km 0.2 0.4 0.6 0.8 1 1.2 1.4 2 4 6 8 10 12 14 16 r [µm] (c) z = 1.0 km

2-D kinematic simulations

Droplet-size PDF

0.3 0.6 0.9 1.5 0.3 0.6 0.9 1.2 1.5 z (km) x (km) 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Liquid-water mixing ratio (g/kg) (a) (b) (c)

0.2 0.4 0.6 0.8 1 1.2 1.4 (a) z = 1.4 km non-turbulent ε = 10-3 m2 s-3 0.2 0.4 0.6 0.8 1 1.2 PDF(r) [µm-1] (b) z = 1.2 km 0.2 0.4 0.6 0.8 1 1.2 1.4 2 4 6 8 10 12 14 16 r [µm] (c) z = 1.0 km

Microphysical profiles

horizontally averaged

0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

• 0.1 -0.05

0.05 0.1 z (km) 〈S〉 (%) 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 0 0.2 0.4 0.6 0.8 1 Ndroplets / NCCN non-turbulent turbulent 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 0 0.5 1 1.5 2 2.5 3 3.5 σr [µm]

Summary and outlook

◮ Simple model to mimic SGS variability ◮ Straightforward for super-droplets, difficult for bin

microphysics

◮ Important for rain development through collision/coalescence ◮ Thermodynamic feedback: extends the distance of activation ◮ Future: couple the SGS scheme with dynamic LES

Acknowledgements

Vertical velocity fluctuations

Stationary homogeneous isotropic turbulence

W ′(t) = 0 W ′(0)W ′(t) = σ2

W ′ exp (−|t|/τm)

L ε = ν(∇u)2

Kolmogorov scaling (inertial subrange) σ2

W ′ ∼ (Lε)2/3

τm ∼ L2/3 ε1/3

Super-droplets (SDs)

Shima et al. (2009), Arabas et al. (2015)

Ndroplets ∼ 1011 − 1014

1 3 2 1 1 1 1 1 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2

10 − 100 meters

◮ Multiplicities:

ξ1 = 6, ξ2 = 10, . . .

◮ SDs have the same attributes

(r, S′, W ′, . . .)

◮ Well-mixed

Aerosol indirect effect

induced by turbulence

0.02 0.04 0.06 0.08 0.1 0.12 0.14 5 10 15 20 25 30 35 40 NCCN = 25 cm-3 50 100 200 300 τm ≈ 45 s τc ≈ 8 s τc ≈ 1 s PDF(r > rc) [µm-1] r [µm]

◮ fast × slow microphysics

dS′ dt = − S′ τS + aW ′(t), τS ∼ min{τc, τm}

Chandrakar et al., PNAS, 113 (2016); Siebert and Shaw, JAS, 74 (2017)

Evolution of the moments

4 8 12 16 20 〈r〉 (µm) (a) adiabatic, non-turbulent adiabatic, turbulent entraining, non-turbulent entraining, turbulent 4 8 12 16 20 1 2 3 4 200 400 600 800 1000 σr (µm) t (s) (b) 1 2 3 4 200 400 600 800 1000

Sensitivity to other model parameters

0.04 0.08 0.12 0.16 τt ≈ 40 s (a) ε = 101 cm2 s-3 ε = 102 cm2 s-3 ε = 103 cm2 s-3 0.04 0.08 0.12 L ≈ 50 m PDF(r > rc) [µm-1] (b) ε = 101 cm2 s-3 ε = 102 cm2 s-3 ε = 103 cm2 s-3 0.04 0.08 0.12 5 10 15 20 25 r [µm] (c) <w> = 0.5 m s-1 <w> = 1.0 m s-1 <w> = 2.0 m s-1

Sensitivity to other model parameters

0.04 0.08 0.12 (a) λ = 50 m λ = 100 m λ = 200 m 0.04 0.08 0.12 PDF(r > rc) [µm-1] (b) σ = 0.05 σ = 0.10 σ = 0.20 0.04 0.08 0.12 5 10 15 20 25 r [µm] (c) RH = 0.50 RH = 0.65 RH = 0.80