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. Abade 1 , W. W. Grabowski 2 , H. Paw� lowska 1 1 University of Warsaw, Faculty of Physics, Institute of Geophysics, Warsaw, Poland 2 National 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 LES grid box Droplet growth moist air d r d t = 1 water r D � S � droplet ∆ r Mean-field supersaturation � S � = e − 1 e s ∆ ∆ ∼ tens of meters (inertial range)

Microphysical variability at sub-grid scales (SGS) ◮ S = � S � + S ′ ◮ Entrainment of unsaturated air + CCN Entraiment Entraiment ◮ SGS mixing CCN ◮ Activation/deactivation ◮ Lagrangian method

Stochastic growth K¨ ohler curve and potential S c stable unstable S eq ( r ) r d r � S − A r + B � d t = D r 3 Koehler curve 0 x ≡ r 2 S = � S � + S ′ Koehler potential V ( r ) 〈 S 〉 < S c 〈 S 〉 = S c 〈 S 〉 > S c d x d t = − ∂V ∂x + 2 DS ′ r d 0.1 r c 1 10 r [ µ m]

Stochastic activation and growth driven by supersaturation fluctuations S c S eq ( r ) r d r � S − A r + B � d t = D 0 r 3 haze cloud droplet droplet 0 < 〈 S 〉 < S c x ≡ r 2 S = � S � + S ′ V 〈 S 〉 ( r ) SA SDA d x d t = − ∂V r d r 1 r c r 2 ∂x + 2 DS ′ r Stochastic activation (SA) / deactivation (SDA)

Supersaturation and velocity fluctuations d S ′ d t = − S ′ − S ′ i i i + aW ′ i ( t ) τ c τ m T and p 1 τ c ∼ (condensation) � W � W ′ decreasing DN � r � i S i τ m ∼ eddy turnover time (mixing) ◮ Statistics of W ′ ( t ) ? Grabowski and Abade, JAS, 74 (2017)

Entraining cloud parcel stochastic entrainment events � W � cooler λ ∼ 200 m decreasing pressure and temperature entraiment of unsaturated air entrainment rate µ = 1 d m + CCN cool LCL m d t warm Krueger et al. , JAS, 54 (1997); Romps and Kuang, JAS, 67 (2010)

Droplet-size distribution after a 1-km parcel rise 0.3 (a) adiabatic, non-turbulent 0.25 PDF( r > r c ) ( µ m -1 ) adiabatic, turbulent 8.8 entraining, non-turbulent 0.2 entraining, turbulent 0.15 0.1 0.05 0 1 (b) PDF( r ) ( µ m -1 ) 0.1 0.01 0 5 10 15 20 25 r ( µ m)

Stochastic CCN activation adiabatic parcel

Stochastic CCN activation 1 1 1 1 (a) (c) Adiabatic parcel Entraining parcel 0.5 0.5 0.5 0.5 〈 S 〉 (%) 〈 S 〉 (%) 0 0 0 0 -0.5 -0.5 -0.5 -0.5 adiabatic non-turbulent entraining non-turbulent adiabatic turbulent entraining turbulent -1 -1 -1 -1 (b) (d) 1 1 1 1 0.8 0.8 0.8 0.8 N c / N CCN N c / N CCN 0.6 0.6 0.6 0.6 0.4 0.4 0.4 0.4 0.2 0.2 0.2 0.2 0 0 0 0 0 0 50 50 100 100 150 150 200 200 0 0 50 50 100 100 150 150 200 200 t [s] t [s]

2-D kinematic simulations 1.5 ◮ Prescribed flow u ( r ) 1.2 ◮ Balance equations for entropy LCL 0.9 and water vapor z (km) 0.6 ◮ Super-droplets 0.3 ◮ ǫ = 10 − 3 m 2 s − 3 everywhere 0 0 0.3 0.6 0.9 1.2 1.5 x (km)

2-D kinematic simulations 1.5 ◮ Prescribed flow u ( r ) 1.2 ◮ Balance equations for entropy LCL 0.9 and water vapor z (km) 0.6 ◮ Super-droplets 0.3 ◮ ǫ = 10 − 3 m 2 s − 3 everywhere 0 0 0.3 0.6 0.9 1.2 1.5 x (km)

2-D kinematic simulations Droplet-size PDF 1.5 0.8 1.4 (a) z = 1.4 km 1.2 1 0.7 0.8 non-turbulent ε = 10 -3 m 2 s -3 1.2 0.6 0.4 0.6 0.2 Liquid-water mixing ratio (g/kg) 1.2 0.5 (b) z = 1.2 km 0.9 1 PDF( r ) [ µ m -1 ] 0.8 z (km) 0.4 0.6 0.4 0.6 0.2 0.3 1.4 (c) z = 1.0 km 1.2 0.2 1 0.3 0.8 0.6 0.1 0.4 0.2 0 0 0 2 4 6 8 10 12 14 16 0 0.3 0.6 0.9 1.2 1.5 r [ µ m] x (km)

2-D kinematic simulations Droplet-size PDF 1.5 0.8 1.4 (a) (a) z = 1.4 km 1.2 1 0.7 0.8 non-turbulent (b) ε = 10 -3 m 2 s -3 0.6 0.6 0.4 0.2 Liquid-water mixing ratio (g/kg) (c) 1.2 0.5 (b) z = 1.2 km 0.9 1 PDF( r ) [ µ m -1 ] 0.8 z (km) 0.4 0.6 0.4 0.6 0.2 0.3 1.4 (c) z = 1.0 km 1.2 0.2 1 0.3 0.8 0.6 0.1 0.4 0.2 0 0 0 2 4 6 8 10 12 14 16 0 0.3 0.6 0.9 1.2 1.5 r [ µ m] x (km)

Microphysical profiles horizontally averaged 1.5 1.5 1.5 non-turbulent turbulent 1.4 1.4 1.4 1.3 1.3 1.3 1.2 1.2 1.2 z (km) 1.1 1.1 1.1 1 1 1 0.9 0.9 0.9 0.8 0.8 0.8 -0.1 -0.05 0 0.05 0.1 0 0.2 0.4 0.6 0.8 1 0 0.5 1 1.5 2 2.5 3 3.5 〈 S 〉 (%) N droplets / N CCN σ r [ µ m]

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 ) � = σ 2 W ′ exp ( −| t | /τ m ) Kolmogorov scaling (inertial subrange) L τ m ∼ L 2 / 3 W ′ ∼ ( Lε ) 2 / 3 σ 2 ε 1 / 3 ε = � ν ( ∇ u ) 2 �

Super-droplets (SDs) Shima et al. (2009), Arabas et al. (2015) N droplets ∼ 10 11 − 10 14 ◮ Multiplicities: 3 2 3 1 1 3 3 ξ 1 = 6 , ξ 2 = 10 , . . . 3 3 2 2 3 2 1 3 ◮ SDs have the same attributes 3 3 3 2 2 1 2 3 ( r, S ′ , W ′ , . . . ) 3 3 2 1 1 2 3 2 ◮ Well-mixed 10 − 100 meters

Aerosol indirect effect induced by turbulence 0.14 τ m ≈ 45 s 0.12 300 200 PDF( r > r c ) [ µ m -1 ] 0.1 τ c ≈ 1 s 100 50 0.08 N CCN = 25 cm -3 0.06 0.04 τ c ≈ 8 s 0.02 0 0 5 10 15 20 25 30 35 40 r [ µ m] ◮ fast × slow microphysics d S ′ d t = − S ′ + aW ′ ( t ) , τ S ∼ min { τ c , τ m } τ S Chandrakar et al. , PNAS, 113 (2016); Siebert and Shaw, JAS, 74 (2017)

Evolution of the moments 20 20 (a) 16 16 〈 r 〉 ( µ m) 12 12 adiabatic, non-turbulent 8 8 adiabatic, turbulent entraining, non-turbulent 4 4 entraining, turbulent (b) 4 4 3 3 σ r ( µ m) 2 2 1 1 0 0 0 0 200 200 400 400 600 600 800 800 1000 1000 t (s)

Sensitivity to other model parameters 0.16 ε = 10 1 cm 2 s -3 (a) ε = 10 2 cm 2 s -3 0.12 ε = 10 3 cm 2 s -3 0.08 τ t ≈ 40 s 0.04 0 PDF( r > r c ) [ µ m -1 ] ε = 10 1 cm 2 s -3 (b) ε = 10 2 cm 2 s -3 0.12 ε = 10 3 cm 2 s -3 0.08 L ≈ 50 m 0.04 0 <w> = 0.5 m s -1 (c) <w> = 1.0 m s -1 0.12 <w> = 2.0 m s -1 0.08 0.04 0 0 5 10 15 20 25 r [ µ m]

Sensitivity to other model parameters (a) λ = 50 m 0.12 λ = 100 m λ = 200 m 0.08 0.04 0 PDF( r > r c ) [ µ m -1 ] (b) σ = 0.05 0.12 σ = 0.10 σ = 0.20 0.08 0.04 0 (c) RH = 0.50 0.12 RH = 0.65 RH = 0.80 0.08 0.04 0 0 5 10 15 20 25 r [ µ m]