? entrainment-detrainment environmnet Asymptotic limit: s c -> 0

Transcription

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

2 SCA: segmentally-constant Approximation w c, q c,.j c w e, q e,.j e x Convective Updarft Environment

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4 Segmentally-Constant Approximation (SCA)+Nonhydrostatic Anelastic Model (NAM): NAM-SCA Temperature Anomaly (K)

5 Never Go Backwards: I. Use of Entrainment-Detrainment in Prognostic Formulation

6 SCA-Plume Experiments (NAM-SCA, Yano and Baizig 202) Fixed interface: Lagrangian:

7 Fixed interface Fractional Entrainment- Detrainment Rate Lagrangian K

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

9 Experiment with Entraining-Plume Hypothesis:

10 A General SCA-based Approach+Entrainment-Detrainment (Yano, 202 GMD): Multi-Component Flow Analogy :Primitive Eq. System

11 Segmentally-Constant Approximation (SCA)+Nonhydrostatic Anelastic Model (NAM): NAM-SCA Temperature Anomaly (K)

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

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

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

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

16 Simulation Errors for NAM-SCA-SCM (GATE): ACCESS: ECHAM: NB: Smaller Domains with Lower Resolutons Often Work the Best

17 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, 3,

18 erformance of Quasi-Equilibrium based arameterizations: Observed Convective Precipitatoin: GATE: ACCESS (Australian UM): GATE: TWP-ICE: TWP-ICE:

19 Performance of Quasi-Equilibrium based Parameterizations: ACCESS (Australian UM): GATE: ECHAM: GATE: TWP-ICE: TWP-ICE:

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

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

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23 ..A General Strategy for PDF(DDF) Approach

24 Mode decomposition: take when subgrid-scale processes have clear structures (e.g., boundary-layer wake, plume, convective towers, mesoscale organization) choose a mode set (Fourier, wavelet, EOF, etc) NB: the set must represent the subgrid structures well apply a high truncation (prototype model for a parameteriztion, prognostic scheme: NAM-SCA) further approximations: e.g., for mass-flux formulation: Entrainment-detrainment, environment, s -> 0

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26 Segmentally-Constant Approximation (SCA): example for Mode Decomposion: Fully-prognostic prototype model for the mass-flux parameterization:

27 Structure of Mass-Flux Convection Paprameterization: Ingredients: Hot Towers: SCA :NAM-SCA entrainment-detrainment environmnet Asymptotic limit: s c -> 0 Closure

28 Structure of Mass-Flux Convection Paprameterization: Ingredients: Hot Towers: SCA :NAM-SCA entrainment-detrainment environmnet Asymptotic limit: s c -> 0 Closure

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

30 Entraining Plume Hypothesis: Laboratory Experiments (Morton et al., 956)

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33 Varioius Possibilities for Entrainmnet- Detrainment Hypotheses (cf., de Rooy et al, 203, QJ): after Raymond,993 undiluted entraining plume cloud top entrainment stochastic mixing Hot tower Stommel (95) Paluch (979) Raymond & Blyth (986)

34 Environement-Convection Separation convective Environment elements

35 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

36 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)?

37 Closure Problem (cf., Yano et al., 203, ACP): Two Major Possibilities based on conservation laws: Moisture (Kuo 974) Energy Cycle: CAPE, Cloud Work Function (Arakawa and Schubert, 974, Yano and Plant 202a, b, Plant and Yano 203) NB: Trigger and Suppression are NOT a Formal Part of Clousre (cf., Yano et al., 203, ACP)

38 Moncrieff s Archetype Convection Representation (992): NAM-SCA Framework can numerically generate an archetype for a given environmental state (Cubism Version)

39 Robust Strategy (Recipe) for Parameterization Development: Start from Basic Set of Eqs: CRM/LES Systematic Strategy: e.g., Mode Decomposition + Compression = SCA 0 th -Order Finite Volume + Adaptivity Mesoscale Archetype (cf., Moncrieff)?

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

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

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

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

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

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

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

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

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

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