Observational and Numerical Studies on Turbulent Entrainment-Mixing

Transcription

1 Observational and Numerical Studies on Turbulent Entrainment-Mixing Processes Chunsong Lu 1, 2, Yangang Liu 1, Shengjie Niu 2, Steven Krueger 3, Seong Soo Yum 4, Satoshi Endo 1, Timothy Wagner 5 1. Brookhaven National Laboratory, New York 2. Nanjing University of Information Science and Technology, Jiangsu, China 3. University of Utah, Salt Lake City, Utah 4. Yonsei University, Seoul, Korea 5. Creighton University, Omaha, Nebraska

2 Motivations (1) Entrainment-mixing gprocesses affect (1) warm-rain initiation (2) aerosol indirect effect (3) cloud-climate feedback (4) radar retrieval of liquid water content Our understanding regarding entrainment- mixing processes is far from complete.

3 Motivations (2) Question One: How fast is dry air entrained into clouds? Entrainment Rate Question Two: How does cloud microphysics respond to entrained dry air? Question Three: How to represent entrainment- mixing mechanisms in models? Entrainment Mixing Mechanisms Parameterization

4 Question One How fast is dry air entrained into clouds? Entrainment Rate

5 New Entrainment Rate Estimation Approach for Cumulus 1 dm m dz λ: entrainment rate m: mass of a cloud parcel z: height z m( z) dm dz m m( z) ln m ( z ) z 0: cloud base height z 0 m( z0) 0 mz ( ) ln h =z-z 0 mz ( 0) ln χ= m(z 0 )/m(z) : mixing z z0 h fraction of adiabatic cloud Lu et al., 2012, GRL

6 Estimation of Mixing Fraction χ (1) Total water (q t ) conservation: q q * q (1 *) t t _ cloud t _ environment (2) Liquid water potential temperature (θ l ) conservation: * (1 *) l l _ cloud l _ environment

7 Validation with Aircraft Observations Non-drizzling cumuli in RICO (Rain in Cumulus over the Ocean) (Gerber et al., 2008) Traditional Approach (Betts, 1975): c / z e Entrainment rate Value of a conserved c property in cloud c The new approach has smaller uncertainties. e Value of a conserved property in environment z Height

8 Validation with LES Results A benchmark case over the SGP site simulated by an LES model, WRF-FASTER. The result from the new approach is between the results from the traditional approaches.

9 Question Two How does cloud microphysics i respond to entrained dry air? Entrainment Mixing Mechanisms

10 Microphysics: Entrainment-Mixing Types Homogeneous Entrainment-Mixing Entrained Drier Air Unmixed Cloudy Air e.g., Baker and Latham,1979; Baker et al.,1980; Yum, Just Saturated Air by Droplet Evaporation Unmixed Inhomogeneous Entrainment-Mixing with Subsequent Ascent Extreme Inhomogeneous Entrainment-Mixing t i

11 Dynamics: Damkoehler Number Damkoehler number: Da / mix react Entrained Drier Air Unmixed Cloudy Air τ mix : the time needed for complete turbulent homogenization of an entrained parcel of size L (Baker et al., 1984): mix ~( L /ξ) 2 1/3 ξ: dissipation rate τ react : the time needed for droplets to evaporate in the entrained dry air or the entrained dry air to be saturated (Lehmann et al. 2009): dr dt m A s r m ds B s dt r m : mean radius s: supersaturation

12 Dynamics: Transition Scale Number Lehmann et al. (2009) defined transition length (L*) by setting Lehmann et al. (2009) Da =1. Homogeneous η Inhomogeneous L* Da / 1 mix ~( L mix L /ξ) react 2 1/3 1/ 2 3/ 2 * react We define transition scale number (N L ) as (Lu et al., 2011): L* react A larger value of N L indicates a N L higher probability of homogeneous mixing. Kumar et al. (2012) 1/ 2 3/ 2 η: Kolmogorov scale

13 Aircraft Observational Data Stratocumulus (Cloud Intensive Observation Period) Time: March 2000 Site: Southern Great Plains (SGP), USA Instrument: Forward Scattering Spectrometer Probe (1Hz) Cumulus (RACORO) Time: January to June 2009 Site: Southern Great Plains (SGP), USA Instrument: Cloud and Aerosol Spectrometer (10 Hz)

14 Microphysics vs Dynamics ---Stratocumulus(1) Extreme inhomogeneous mixing Homogeneous mixing Leg March 2000 Leg March Leg March Leg March One dominant mechanism can not rule out the occurrence of the others.

15 Microphysics vs Dynamics 层积云中的过渡尺度数 ---Stratocumulus(2) The leg affected by homogeneous mixing has the largest N L. Inhomogeneous entrainment-mixing t i i mechanism dominates in stratocumulus.

16 Microphysics vs Dynamics 积云中的过渡尺度数 ---Cumulus N L has a transition itself. Homogeneous entrainment-mixing t i i mechanism dominates in cumulus.

17 Question Three How to represent entrainmentmixing mechanisms in models? Parameterization

18 Microphysics vs Dynamics ---Stratocumulus(2) Extreme inhomogeneous mixing Homogeneous mixing Leg March 2000 Leg March Leg March Leg March Different entrainment-mixing mechanisms occur simultaneously. It s critical to determine homogeneous mixing degree.

19 Flow Chart of Entrainment Mixing Parameterization ti? Homogeneous Mixing Degree? Transition Scale Number Current Cloud Parameterization

20 Homogeneous Mixing Degree --- Ψ 1 Dilution 1 /2 Similar to Figure 5 in Krueger (2008) Homogeneous: Ψ 1 =1; extreme inhomogeneous: Ψ 1 =0.

21 Homogeneous Mixing Degree --- Ψ 2 2, Ψ 3 N N r r ( i v va 3 3 ) 2 Nh Ni rvh rva ln N ln N ln r ln r 3 3 i v vi ln Nh ln Ni ln rvh ln rvi Ψ 3 turns out to be related to α: 3 where α was defined by Morrison and Grabowski (2008): q N N ( ) q

22 Two Transition Scale Numbers (1) Lehmann et al. (2009) defined transition length (L*) by setting Lehmann et al. (2009) Da =1. Homogeneous η Inhomogeneous L* A larger value of N L indicates a higher probability of homogeneous process. Da / 1 mix ~( L mix L /ξ) react 2 1/3 1/ 2 3/ 2 * react We define transition scale number (N L ) as (Lu et al., 2011): N L L* 1/ 2 η: Kolmogorov scale 3/ 2 react

23 Two Transition Scale Numbers (2) τ react is the time when r <0 or s > dr s d l t di A dt r ds dt Brs r: droplet radius; s: supersaturation; A: a function of pressure and temperature; B: a function of pressure, temperature and droplet number concentration (N a or N 0 ). Dry air + = N a N 0 Scale Number N La N L0

24 Flow Chart of Entrainment Mixing Parameterization ti Homogeneous Mixing Degree? Transition Scale Number Current Cloud Parameterization

25 Explicit Mixing Parcel Model (EMPM) Domain size: 20 m m m ; Adiabatic Number Concentration: 102.7, 205.4, 308.1, 410.8, cm -3 ; Relative humidity: 11%, 22%, 44%, 66%, 88%; Dissipation rate: 1e-5, 5e-4, 1e-3, 5e-3, 1e-2, 5e-2 m 2 s -3 ; Krueger (2008) Mixing fraction of dry air: 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9.

26 Homogeneous Mixing Degree vs. Scale Numbers Red: N L0 Blue: N La 1 Ψ h th ti ht t l ti hi t th l b 1. Ψ 1 has the tightest relationship to the scale numbers. 2.Ψ 2 and Ψ 3 are close to each other.

27 Flow Chart of Entrainment Mixing Parameterization ti Homogeneous Mixing Degree Transition Scale Number Current Cloud Parameterization

28 Summary--- Question One A new approach is presented to estimate entrainment rate in cumulus clouds. The approach s advantages: (1) smaller uncertainties. (2) no need to measure in-cloud temperature and water vapor. (3) the potential for developing a remote sensing technique to infer entrainment rate profiles.

29 Summary--- Question Two In stratocumulus, inhomogeneous entrainmentmixing mechanism dominates based on 1 Hz data; In cumulus, homogeneous entrainment-mixing mechanism dominates based on 10 Hz data; The domination of one mechanism cannot rule out the occurrence of the others. A larger transition scale number generally corresponds to homogeneous entrainmentmixing mechanism.

30 Summary--- Question Three Three measures of homogeneous mixing degree are defined; they are positively correlated with scale numbers based on the EMPM results; The positive relationships can be used to explore the parameterization of entrainment- mixing mechanisms.

31 Future Work Simulate the DNS cases (Kumar et al., 2012) with the Explicit Mixing Parcel Model (EMPM). Apply the mixing fraction approach to estimate entrainment rate in shallow cumulus clouds to obtain statistical result of entrainment rate.

32 Acknowledgments Dr. Hermann Gerber at the Gerber Scientific Inc., Dr. Pavel Romashkin and Allen Schanot at NCAR, Prof. Mike Poellot, Prof. Tony Grainger and Mr. Andrea Neumann at UND. Cloud IOP, RACORO and RICO crew. supported by the DOE Earth System Modeling (ESM) program via the FASTER project and Atmospheric System Research (ASR) program.

33 Thanks!