Evolution of the cloud droplet size distribution under the effect of turbulence

1. Evolution of the cloud droplet size distribution under the effect of turbulence Charmaine Franklin Bureau of Meteorology Research Centre Melbourne, Australia

2. Outline • Why is an accurate collision-coalesence rate of cloud droplets important? • Development of turbulent collision kernel (work from postdoc at McGill University with Paul Vaillancourt and Peter Yau) • Effects of turbulent collision kernel on evolution of the drop size distribution • Development of autoconversion parameterisation that includes the effect of turbulence • Comparison with other autoconversion models

3. Motivation • Autoconversion of cloud droplets to rain drops is one of the key process that determines cloud liquid water path, precipitation and cloud cover - implications for both NWP and climate • Warm rain accounts for 31% of total rain in tropics and 72% rain area • Autoconversion also important for mixed phase clouds as impacts the formation of hail/graupel • Theoretical droplet growth times are too slow to describe observed onset of precipitation • Turbulence has been recognised to play a role in autoconversion process for over half a century and may reduce the growth time of rain drops

4. Turbulent collision kernel N=80, Rl=33 N=240, Rl=55 e=95 cm2 s-30= 0.45 su’=13 cm s-1tk=0.04 s vk=2.0 cm s-1 e=1535 cm2 s-30= 0.45 su’=39 cm s-1tk=0.01 s vk=4.0 cm s-1 • Empirical model based on DNS of turbulent flows and explicit tracking of large numbers of droplets • Flow dissipation rates of TKE 100 – 1500 cm2 s-3 • Collector droplets in size range 10 – 30 m radius details in Franklin, Vaillancourt and Yau (2006) JAS, in press

5. Collision kernel- measures the rate of collisions between two particle size groups normalised by their number concentrations Average collision kernel is described as the average volume of fresh fluid entering the collision sphere per unit time R = relative radial velocity

6. Preferential concentration (clustering) 20mm radius 10mm radius - cloud droplets have finite inertia, interactions with flow produce spatial correlations - g(R) is the radial distribution function • similar to clustering index, calculates the mean-variance ratio - g(R)=1 for random distribution - g(R)>1 if clustering

7. Turbulent collision kernel parameterisation cm3 s-1 cm s-1 where is the droplet terminal velocity, is the Kolmogorov velocity, is the eddy dissipation rate of TKE (cm3 s-2)

8. Stochastic collection equation • Using Bott’s (1998) SCE solver • Mass doubles after 4 grid cells • 160 bins with drop radii from 0.6 m to 104m • Hydrodynamic kernel of Hall (1980) • Terminal velocities of Beard (1976) • Collision efficiencies: • collector < 30m Davis (72) Jonas (72) • 40 < collector < 300m, radius ratio < 0.6 Schlamp et al. (76), Lin and Lee (75), Shafrir and Gal-Chen (71) • 40 < collector < 300m, radius ratio > 0.6 Klett and Davis (73) • Turbulent kernel used for collector drops 10-30 m but still use the gravitational collision efficiencies • Coalescence efficiency equal to 1 • Expect turbulence effects on drops > 30 m to start to diminish

9. Increases in collision kernel 100 cm2s-3 500 1000 1500 m m

10. gravity 100 500 1000 1500 Temporal evolution of mass weighted mean radius lwc = 1 g m-3 no. conc = 240 cm-3 dispersion = 0.5 mean vol radius ~ 10m • time at which rg = 200m m time(sec)

11. gravity 100 500 1000 1500 Temporal evolution of effective radius • time when effective radius equals 40 m m Slingo (90) showed that reducing reby 2mcan offset the warming effect caused by doubling CO2 time (min)

12. Effect of turbulent collision efficiency ec2 ec increase • Assume collision efficiency increases as a function of eddy dissipation rate of TKE • Test two cases: moderate increase and large increase • ec1 increases the gravitational collision efficiencies by 1.1 – 1.3 times as fn of  • ec2 increases by 1.1 – 2.0 times ec gravity ec1 dissipation rate of TKE (cm2 s-3)

13. gravity 100 500 1000 1500 gravity 100 500 1000 1500 Effect of turbulent collision efficiency on reflectivity dBZ ec1 increased by 1.1 - 1.3 ec original time (min) ec2 increased by 1.1 – 2.0

14. gravity turbulence rel. velocity clustering Contribution of turbulence effects - clustering and velocity 500 100 cm2s-3 fraction of mass > 40m 1000 1500 time (min)

15. Autoconversion parameterisation that includes turbulent collision kernel • Solve SCE for liquid water contents 0 < lwc 2 g m-3, number concentrations 500 cm-3 and relative dispersion coefficients of the initial DSD 0.25dispersion0.4 • Gamma function • is calculated as the rate of change at which the cloud droplets are colliding to form raindrops • Threshold radius 40 m – good agreement with exponents from Wood (05) data • Difference to Beheng (94) is that we cover smaller lwc and also include turbulent collision kernels as well as a different solver • By covering a broad range of lwc, no. conc. and initial spread of DSD, we increase the range of applicability and statistical meaning of the results

16. Empirical model of autoconversion • where is rain water, is cloud water, is cloud number concentration

17. Empirical model Larger power reflects a sharper gradient and more of a Kessler type Heaviside function • where is rain water, is drop mean volume radius

18. Empirical model (Manton and Cotton 1977) includes the collision efficiency, Stokes constant, drop mean volume radius is the mean collision efficiency, usually taken to be ~ 0.5 Baker (93) estimated that this can overestimate the rate by 1-2 orders • where is rain water, is cloud water, is cloud number concentration

19. Comparison with other models lwc 1 g m-3, 50 drops, dispersion 0.4 parameterised • SCE data • new gravity param. • Khairoutdinov&Kogan(00) • Beheng (94) • Seifert&Beheng (01) • Liu&Daum (06) =0.1 • Liu&Daum (06) =1 • Liu&Daum (06) =100 SCE data (kg m-3 s-1)

20. Comparison with other models lwc 2 g m-3, 300 drops, dispersion 0.4 parameterised • SCE data • new gravity param. • Khairoutdinov&Kogan(00) • Beheng (94) • Seifert&Beheng (01) • Liu&Daum (06) =0.1 • Liu&Daum (06) =1 • Liu&Daum (06) =100 SCE data (kg m-3 s-1)

21. Comparison with other models lwc 0.5 g m-3, 50 drops, dispersion 0.4 parameterised • SCE data • new gravity param. • Khairoutdinov&Kogan(00) • Beheng (94) • Seifert&Beheng (01) • Liu&Daum (06) =0.1 • Liu&Daum (06) =1 • Liu&Daum (06) =100 SCE data (kg m-3 s-1)

22. Comparison with other models lwc 0.2 g m-3, 50 drops, dispersion 0.25 parameterised • SCE data • new gravity param. • Khairoutdinov&Kogan(00) • Beheng (94) • Seifert&Beheng (01) • Liu&Daum (06) =0.1 • Liu&Daum (06) =1 • Liu&Daum (06) =100 SCE data (kg m-3 s-1)

23. gravity 100 500 1000 1500 Sensitivity to turbulence no. conc. = 100 cm-3 no. conc. = 300 cm-3 no. conc. = 500 cm-3 • no. conc. = 50 cm-3 (kg m-3 s-1) lwc (g m-3)

24. gravity 100 500 1000 1500 Sensitivity to turbulence no. conc. = 100 cm-3 K&K (00) B (94) S&B (01) L&D (06) 0.1 L&D (06) 1 L&D (06)100 no. conc. = 300 cm-3 no. conc. = 500 cm-3 • spread = 0.4 no. conc. = 50 cm-3 (kg m-3 s-1) lwc (g m-3)

25. Summary and future work • Turbulence can accelerate the evolution of the DSD by reducing time to formation of rg= 200 m by up to 20% • More significant is percentage of mass transferred to drop sizes >40 m in 20 minutes – see table • Effect of turbulence is to offset the aerosol indirect effects • Use same data to find accretion parameterisation • Implement new autoconversion-accretion parameterisation into BAM SCM to investigate the impact on the liquid water path, precipitation etc