Structure of Mass-Flux Convection Paprameterization. by Jun-Ichi Yano Meteo France Toulouse

Transcription

1 Structure of Mass-Flux Convection Paprameterization by Jun-Ichi Yano Meteo France Toulouse

2 One cannot be a successful scientist without realizing that, in contrast to the popular conception supported by newspapers and mothers of scientists, a goody number of scientists are not only narrow-minded and dull, but also just stupid." ("Double Helix", James Watson)

3 Basic Reference: J.-I. Yano, J.-L. Redelsperger, F. Guichard, and P. Bechtold, 2005: Mode Decomposition As a Methodology For Developing Convective-Scale Representations in Global Models. Quator. J. Roy. Meteor. Soc, 131,

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5 Structure of Mass-Flux Convection Paprameterization: Outline (Ingredients): Introduction: why we need this? Riehl & Malkus Hot Tower Hypothesis SCA entrainment-detrainment environmnet Asymptotic limit: s c -> 0 Closure

6 What should be parameterized: A Typical Atmospheric Convective System?: ~200km cumulus convection (convective towers) ~20km stratiform clouds (mesoscale)

7 Parameterization Problem: Full System (CRM)? Parameterization (caricature)

8 Q: the subgrid-scale physiccal represnetations (parameterizations)? full physical system: average over the grid-box parameterization? =? (Downscaling)

9 Examples: Heat Equation: Temporal Tendency + Large-Scale Advection = Diabatic Heating + Subgrid-Scale Transport = Q1: Apparent Heat Source? Moisture Equation: Temporal Tendency + Large-Scale Advection = -Condensation + Evaporation +Subgrid-Scale Transport =- Q2: Apparent Moisture Sink?

10 Observational Estimates of Q1and Q2: Deep convection Tropical Pacific Tropical Atlantic Yanai et al., 1973, JAS Yanai and Johnson, 1993 Note the typical tropical maximum of Q1 at 500 hpa, Q2 maximum is lower and typically at 800 hpa

11 Why It Is Important? Because of Its Global Role: Especially over the Tropics (Riehl and Malkus 1958): Hot-Tower Hypothesis (for the Hadley Circulation)

12 Hot-Tower Hypothesis (Riehl and Malkus 1958): Classcial View on Hadley Circulation: Modern View: Eq. lat. Eq. Hot Towers (~5km) lat.

13 Hot-Tower Hypothesis (Riehl and Malkus 1958): arge-scale Upward otion dry entropy Radiative Cooling Entropy Transfer moist entropy

14 Hot-Tower Hypothesis (Riehl and Malkus 1958): Radiative Cooling dry entropy Hot Tower moist entropy

15 Hot-Tower Hypothesis (Riehl and Malkus 1958): Implications: Hot Towers << Large-Scale Cirulation (Hadley-Walker) Parameterization (Convective Parameterization Problem) cf., Scale-Separation Principle

16 Hot towers within a gird box: Basic idea of convection parametrization

17 Hot towers within a Gird Box: Basic idea of Convection Parametrization (Fig. 1, Arakawa and Schubert 1974)

18 Structure of Mass-Flux Convection Paprameterization: Outline (Ingredients): Introduction: why we need this? Riehl & Malkus Hot Tower Hypothesis SCA entrainment-detrainment environmnet Asymptotic limit: s c -> 0 Closure

19 Why It Is Important?: Historical Perspectives Role in Tropical Large-Scale Circulation (Riehl and Markus 1958): Convective Parameterization (Arakawa &Schubert 1974, Kuo 1974, etc) Weather Modification Programme (1960th): Vertification? One-Dimensional Plume Model Natural Laboratory Fluid Laboratory Experiments (ca., ):

20 Historical Evolution of the Study Laboratory Experiments (50-60) 1D Entraining-Plume Model (EPM) (explicit studies) (steady, 60th) (parameterization) Time-depdent 1D EPM (Asai &Kasahara MassFlux ) + Mircophysics (Ogura&Takahashi 1971) Ensemble of Plumes (Arakawa & 2D CRM (70-80) Schubert 1974, etc) 3D CRM (80-90) Cloud Resolving Model (CRM) Comparisons? MassFlux Convective Parameterization

21 Basic Questions Physics: Conditional Instability, CAPE Hot Tower: Plume Model?: Entrainment-Detrainment Convective Parameterization (MassFlux): Convective-Radiative Equilibrium Quasi-Equilibrium Q1, Q2, MassFlux

22 Basic Physics: Complex: Dynamics : Buoyancy-Driven Thermodynamics : Transport=Diffusion +Latent Heating Cloud Microphysics : Rain Formation Chemistry (Aerosoles) : CCN Radiation : Electricity : Solar and Infrared Lightning: Electro-Mgnetic

23 Hot-Tower Hypothesis (Riehl and Malkus 1958): Implications: Hot Towers << Large-Scale Cirulation (Hadley-Walker) Parameterization (Convective Parameterization Problem) cf., Scale-Separation Principle

24 Hot towers within a Gird Box: Basic idea of Convection Parametrization Hot Towers (Convection) Grid Box = Convection+Environment Environment

25 Geometrical Constraint (on CRM): SCA (Segmentally-Constant Approximation) Hot Towers (Convection) :homogeneous inside Environment :homogeneous Grid Box = Convection+Environment

26 SCA: Segmentally-Constant Approximation: Side View w c, q c,.j c w e, q e,.j e x Environment Convective Updarft (Hot Tower)

27 Segmentally-Constant Approximation (SCA) Into Cloud-Resolving Model (CRM) or Nonhydrostatic Anelastic Model (NAM)? : NAM-SCA

28 A Hot Tower (Plume): Segmentally-Constant Approximation (SCA) Into CRM (NAM)? Finite Volume Method Temperature Anomaly (K)

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31 A Hot Tower (Plume): Segmentally-Constant Approximation (SCA) Into CRM (NAM) Temperature Anomaly (K)

32 Generalization of Concept: Hot Towers < Plumes < Convection

33 NAM-SCA: Basic Formulation: mass continuity

34 Simplification of the Horizontal Velocity Calculation: Entrainment-Detrainment Hypothesis

35 Mass Continuity: Vertical Velocity Divergence NAM-SCA: Vertical Velocity Divergence Entrainment-Detrainmnet hypothesis: Prescribed Entrainment-Detrainment Vertical Velocity (MassFlux)

36 Entrainment-Detrainmnet hypothesis: Prescribed Entrainment-Detrainment Vertical Velocity (MassFlux) Mass flux

37 Historical Note: Extensive Laboratory Experiments during 1940s-1950s in order to understand Atmospheric Convection

38 Entraining Plume Hypothesis: Laboratory Experiments (Morton et al., 1956)

39 Entraining Plume Model : Laboratory Experiments (Morton et al 1956) (Turner 1962)

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41 Further Historical Notes: Role in Tropical Large-Scale Circulation (Riehl and Markus 1958): Natural Laboratory Fluid Laboratory Experiments (ca., , Morton,et al) Weather Modification Programme (1960th, Markus-Simpson): Vertification? One-Dimensional Plume Model Convective Parameterization (Arakawa &Schubert 1974, Kuo 1974, etc)

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43 Varioius Possibilities for Entrainmnet- Detrainment Hypotheses (cf., de Rooy et al, 2013, QJ): after Raymond,1993 undiluted entraining plume cloud top entrainment stochastic mixing Hot tower Stommel (1951) Paluch (1979) Raymond & Blyth (1986)

44 Environement-Convection Separation (a hidden assumpotion) convective Environment elements NB: Additional Constraint that can be removed

45 Environement-Convection separation D D E E convective element (a) Environment convective element (b)

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47 MassFlux Parameterization Last Steps: Fractaional area : s c -> 0 Plumes are at steady state: d/dt = 0 NB: the Formulation is timedependent Before taking this Limit

48 Standard Mass-Flux Formulation: M = h(z)m B (t) h(z) : cloud model : steady (no trigger, etc) M B (t) : closure condition: large-scale control NB: if a life-cycle (e.g., trigger) of individual convection is to be consiered, the above formulation is no longer valid (cf., NAM-SCA formulation)?

49 Closure Problem (cf., Yano et al., 2013, ACP): Two Major Possibilities based on conservation laws: Moisture (Kuo 1974) Energy Cycle: CAPE, Cloud Work Function (Arakawa and Schubert, 1974, Yano and Plant 2012a, b, Plant and Yano 2013) NB: Trigger and Suppression are NOT a Formal Part of Clousre (cf., Yano et al., 2013, ACP)

50 Structure of Mass-Flux Convection Paprameterization: Ingredients (Summary): Hot Towers: SCA entrainment-detrainment environmnet Asymptotic limit: s c -> 0 Closure :? :NAM-SCA :? Prognostic? :Quasi-Equilirium (Yano and Plant, 2013, RG) High-Resolution Limit?

51 Further Discussions?: Removal of the Environment Hypothesis : Truncated NAM-SCA

52 A Hot Tower (Plume): Segmentally-Constant Approximation (SCA) Into CRM (NAM) Temperature Anomaly (K)

53 Updraft + Downdraft: A simple demonstration Without environment Hypothesis with w(m/s) NAM-SCA: q(k)

54 Truncated NAM-SCA: More Physical Processes:

55 Truncated NAM-SCA: W (m/s) q (K) qv (g/kg) qc (g/kg) qp (g/kg)

56 Final SCA-Archtype Model? 2D 4-segment model: Axisymmetric 3-segment model:

57 Numerical Archetype: Fixed Distribution of Finite-Volume Elements Cloud Water (g/kg)

58 Tropical Squall-line (GATE Phase III) W (m/s) q (K) qv (g/kg) qc (g/kg) qp (g/kg)

59 When the Entrainment-Detrainment Hypothesis is reintroduced:

60 SCA-Plume Experiments (NAM-SCA, Yano and Baizig 2012) Fixed interface: Lagrangian:

61 Fixed interface Fractional Entrainment- Detrainment Rate Lagrangian K

62 Dependence on Aspect Ratio: Fractional Entrainment- Detrainment Rate K

63 Experiment with Entraining-Plume Hypothesis:

64 In General:?

65 A General SCA-based Approach+Entrainment-Detrainment (Yano, 2012 GMD): Multi-Component Flow Analogy :Primitive Eq. System

66 Robust Basis for Parameterization Closure: Convective Energy Cycle (Yano and Plant 2012a, b, QJ, JAS, Plant and Yano 2013 DAO)

67 Closure Problem in Mass-Flux Formulation (Arakawa and Schubert 1974): Convective Energy-Cycle System: Kinetic Energy Equation (Eq. 132, AS74) Clolud-Work Function Equation (Eq. 142, AS74) Three unkowns: K, M, A A Functional Constraint: K ~ M p (p=2: Pan and Randall, p=1: Yano and Plant) Prognostic Closure based on Energy Cycle NB: Key is to couple the shallow and deep modes under this Formulation in order to properly describe Shallow-to- Deep Transformation (Yano and Plant, accepted to JAS)

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69 Furhter Extension of NAM-SCA: Put More Plumes + Time-Dependent Activation- Deactivation of Plumes (Segments) Highly-Flexible Adaptive Mesh- Refinement: NAM-SCA

70 Activation: interface jump > fac x variance (z)

71 Deactivation: interface jump < facd x variance (z) fac = facd = 1

72 Dry Convective Boundary Layer W (m/s) q (K)

73 Dry Convective Boundary Layer W (m/s) q (K)

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75 More Applications: Archetype Convection Representation

76 Application I: Moncrieff s Archetype Convection Representation (1992)? NAM-SCA Framework can numerically generate an archetype for a given environmental state (Cubism Version)

77 1 1 1 Cloud Water (g/kg) 1 Original NAM-SCA Run

78 1 1 1 Cloud Water (g/kg) 1 NAM-SCA Run in Moving Coordinate

79 1 1 1 Cloud Water (g/kg) 1 NAM-SCA Run in Moving Coordinate: Initial Condition For Archetype

80 Finite-Volume Element Distribution (original) NAM-SCA Run in Moving Coordinate: Initial Condition For Archetype

81 Finite-Volume Element Distribution (smoothed) Numerical Archetype: Fixed Distribution of Finite-Volume Elements

82 1 1 1 Cloud Water (g/kg) 1 NAM-SCA Run in Moving Coordinate: Initial Condition For Archetype

83 Numerical Archetype: Fixed Distribution of Finite-Volume Elements Cloud Water (g/kg)

84 Numerical Archetype: Fixed Distribution of Finite-Volume Elements Cloud Water (g/kg)