UNRESOLVED ISSUES. 1. Spectral broadening through different growth histories 2. Entrainment and mixing 3. In-cloud activation

Transcription

1 URESOLVED ISSUES. Spectral broadening through different growth histories 2. Entrainment and mixing. In-cloud activation /4

2 dr dt ξ ( S ) r, ξ F D + F K 2 dr dt 2ξ ( S ) For a given thermodynamic conditions the rate of growth of a drop s (~r 2 ) is constant. Given the same conditions smaller droplets grow faster (radius) than the large droplets. Condensational growth makes the droplet spectrum to become narrower with height above the cloud base Figures: Brenguier and Chaumat, JAS /4

3 Spectral broadening The observations show broad droplet spectra while the idealized model of droplet growth in an adiabatic convective cell predicts narrow spectra. The r 2 (Φ 2 ) distribution (solid line) for measurements during SCMS (Small Cumulus Microphysics Study, Florida 995). Comparison with the adiabatic reference (dot dashed line). The initial reference spectrum is represented by a dot dashed line on the left. Figures: Brenguier and Chaumat, JAS 200 /4

4 Spectral broadening Spectrum evolution in an adiabatic updraft. The curve labeled C is the corresponding spectrum after condensational growth. Curves labeled C +50 and C -50 are the resulting spectra for a total droplet concentration of C ±50 cm -.. Figures: Brenguier and Chaumat, JAS /4

5 Spectral broadening through different growth histories Simulation of a small cumulus, illustrating the idea of cloud-droplet growth through large-eddy hopping. The figure shows the cloud water field and a small subset of droplet trajectories arriving at a single point at the upper part of a cloud. The trajectories are colored according to the liquid water content encountered. The variability of the vertical velocity across the cloud base already results in some differences in the concentration of activated cloud droplets at the starting point of the trajectories. There are also relatively small-scale changes in color along the trajectories, highlighting variable environments in which the droplets grow. Figure courtesy of S. Lasher-Trapp 5 /4

6 Large eddy-hopping Figure by Katarzyna urowska 6 /4

7 ETRAIMET AD MIXIG OF EVIROMETAL AD CLOUDY AIR

8 RICO (Rain in Cumulus over the Ocean) Cloud water (left) and fraction (right) profiles from the C0 flights during RICO. The sampling included all fligts legs below 2 km for which good data was available. Shown onthe left is the interquartile wariability (25 and 75%, whisker), mean (gray circle) and median (black circle) of cloud-water. The right panel shows estimates of cloud fraction from the lidar (lines) using different detection thresholds (as indicated in red, with the black line being the 22 dbz threshold). The filled circles show cloud fraction from in situ measurements near cloud base (where the sampling was most random) and along the leg at 4.5 km. Cloud water measured in the sub-cloud layer is from precipitation. Medeiros and Stevens 20 8 /4

9 cloud core samples (q l >0, θ v >0 ) cloud samples (q l >0) cloud parcels become negatively buoyant when cooling due to evaporation of cloud droplets due to entrainment drying exceeds entrainment warming 9 /4

10 Entrainment 0 /4

11 Homogeneous mixing const r $ qq s q<q s Inhomogeneous mixing $ r const qq s qq s q<q s qq s qq s qq s /4

12 Inhomogeneous mixing Homogeneous mixing 2 /4

13 extremly inhomogeneous mixing 4 m πρl nrv m rv 4πρ n l number of droplets homogeneous mixing inhomogeneous mixing /4

14 Homogeneous mixing c n/v c e 0 V c, q c V e, q e mixing coefficient concentration after the mixing event n/(v c +V e ) Vc χ Vc + V χ c e water vapor sepcific humidity after the mixing event q q χ + ( χ ) c q e amount of water to be evaporated until the saturation is reached δ LWC ( q q)ρ sat LWC δ LWC 4 πρ r l v r v LWC δ LWC 4 πρ l 4 /4

15 extremly inhomogeneous mixing 4 LWC πρl r 4 qc πρl crv v homogeneous mixing 5 /4

16 LWC LWC ad LWC LWC ad 4 πρl rv 4 πρl r ad ad r rv v,ad v,ad 6 /4

17 Which type of mixing happens in clouds? Turbulence defines how quickly a mixture of dry environmental air and cloudy air is homogeneised " mixing time scale (τ mix ) Evaporation " evaporation time scale (τ evap ). τ mix << τ evap homogeneous mixing τ mix >> τ evap extremly inhomogeneous mixing 7 /4

18 Mixing time scale Kolmogorov scale is the smallest scale in turbulent flow. At the Kolmogorov scale, viscosity dominates and the turbulent kinetic energy is dissipated into heat. Kolmogorov scale: ν k λ ε ν - kinematic viscosity of the fluid, ε-the average rate of dissipation. The rate of dissipation (the ratio of turbulent kinetic energy (~U 2 ) versus the eddy life time (~L/U)): If the initial eddy scale is L, in the intemediate scales λ k < λ < L a cascade of energy from larger to smaller eddies occurs. The rate of evolution of λ is described by a relation: dλ γε λ (Broadwell and Breidenthal, 982) dt γ is a unitless scale (we assume it is equal unity). 4 ε U L 8 /4

19 /4 9 2 mix k 2 k 2 k L mix L 2 L L L 2 d dt d << ε τ λ λ ε λ ε λ τ λ ε λ λ When the eddy scale approaches the Kolmogorov scale, the mixture becomes homogeneized due to the molecular diffusion. The characteristic scale of molecular diffusion is (D molecular diffusion coefficient): 2 mix 2 mix dif 2 k dif ScRe UL D DU L D D τ ν ν τ ν ε ν τ λ τ Schmidt number; for gases Sc~ Reynolds number; large values in the atmosphere dif τ mix τ <<

20 Evaporation time scale dr dt τ evap AS A( RH ) r r 2 r A( RH ) 20 /4

21 /4 2 Dorota Jarecka; PhD thesis evap mix v0 vf 0 f v0 vf 0 f r r d d r r d d τ τ χ Slope coefficient

22 extremly inhomogeneous mixing Inhomogeneous mixing f 0 q q cf co α homogeneous mixing α 0 : f 0 homogeneous mixing α : extremly inhomogeneous mixing 22 /4

23 /4 2 α α α α v0 vf 0 f v0 0 vf f 0 f co cf 0 f r r r r q q In the model, during one time step the value of the mean volume radius doesn t change a lot; one can express is as a Taylor series for (r f /r 0 ). α α χ α α + r r d d r r v0 vf 0 f v0 vf 0 f evap mix evap mix τ τ τ τ α +

24 Shallow convection BOMEX (Barbados Oceanographic and Meteorological Experiment) homogeneous mixing inhomogeneous mixing Dorota Jarecka, PD thesis 24 /4

25 Stratocumulus (EUCAARI IMPACT) Dorota Jarecka, PhD thesis 25 /4

26 Dorota Jarecka, PhD thesis 26 /4

27 Stratocumulus (EUCAARI IMPACT) homogeneous mixing inhomogeneous mixing Dorota Jarecka, PhD thesis 27 /4

28 homoheneous mixing inhomogeneous mixing Dorota Jarecka PfD thesis 28 /4

29 I-CLOUD ACTIVATIO

30 RICO (Rain in Cumulus over the Ocean) Arabas et al. GRL 2009 Gerber et al., JMSJ, /4

31 How is it possible that the dilution of the cloud water content is OT accompanied by the dilution of the droplet concentration? /4

32 How is it possible that the dilution of the cloud water content is OT accompanied by the dilution of the droplet concentration? In-cloud activation (i.e., activation above the cloud base)! 2 /4

33 LES modeling with 2-moment microphysics Slawinska et al., JAS 20 /4

34 In-cloud activation? Grabowski, W.W. and S. A. McFarlane, 2007: Optical properties of shallow tropical cumuli derived from ARM ground-based remote sensing, Geophys. Res. Let. 4 /4