Downscaling and Parameterization. by Jun-Ichi Yano

Transcription

1 Downscaling and Parameterization by Jun-Ichi Yano

2 main references: 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, J.-I. Yano, 2010, Downscaling, Parameterization, Decomposition, Compression: A Perspective from the Multiresolutional Analysis. Adv. Geophy., 23,

3 Focus: Convective Precipitating Systems Key Words: Subgrid-Scale Representation Downscaling, Parameterization Probability (Bayesian) Data Assimilation Mass Flux NAM-SCA

4 Focus: Convective Precipitating Systems Key Word: Subgrid-Scale Representation

5 Focus: Convective Precipitating Systems Key Word: Subgrid-Scale Representation

6 Subgrid-Scale Representation Subgrid-Scale? Model Resolution Explicit Horizontal Scale

7 Downscaling: Subgrid-scale space-time details (e.g., Rainfall Distribution) Parameterization: Feedbacks of subgrid-scale processes to the resolved scales (e.g., Condensative Heating Rate)

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9 Subgrid-Scale Physical Representation: full physical system: average over the grid-box =Q parameterization? =?: Downscaling

10 Downscaling Global Model Subgrid-Scale Processes Parameterization (e.g., Rainfall)?

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14 Questions: Why the current downscaling and parameterization don t mutually work as inverse operations? How to construct the downscaling and parameterization together consistently?: Representation Problem

15 Example of subgrid-scale physical processes: Atmospheric Convection: Full System? (CRM) Representation

16 How to construct a subgrid-scale representation consistently? 1. Identify the Basic Elements for subridscale processes (e.g., plume) 2. Mode Decomposition (efficient representation): Mode=Basic physical elements 3. Compression (mode truncation): Parameterization 4. Decompression (inversion to the physical space): Downscaling

17 Mode Decomposition : Mode Decomposition: where χ l (x,y) :modes (l = 1,.N) :expansion coefficients e.g., Fourier Mass-Fluxes (convection) Basins (hydrology) Wavelets (multiresolutional analysis)

18 Subgrid-Scale Representation Problem: Downscaling Compression parameterization Physical Space Decompression? Compressed Space (e.g., MassFlux)

19 NB: Basic Set of Modes must be chosen so that it fits well to the geometrical structures of the subgrid-scale processes

20 What should be Represented?: ~200km cumulus convection (convective towers) ~20km stratiform clouds (mesoscale) Ensemble of «Plumes»

21 Ensemble of «Plumes»: Spatially-localized features of various different scales (e.g., convective updrafts, downdrafts, mesoscale organizations) A Particular Mode Decomposition Approach: Multiresolutional Analysis e.g., Wavelet

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24 Limit of the Wavelet Approach: Difficulty of Efficient Real (physical) Space Manipulation: Plume (MassFlux) Decomposition

25 Single Plume (MassFlux) Mode : Segmentally-Constant Approximation (SCA) w c, θ c,.ϕ c w e, θ e,.ϕ e x Convective Plume Environment

26 Plumes: Segmentally-Constant Approximation (SCA) Temperature Anomaly (K)

27 NAM-SCA NAM:Nonhydrostatic Anelastic Model

28 Plumes: Segmentally-Constant Approximation (SCA) Temperature Anomaly (K)

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

30 Truncated NAM-SCA: More Physical Processes:

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

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

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

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

35 Downscaling and Parameterization [Summary] Two closely linked operations Downscaling is a pre-condition for Parameterization Parameterization implicitly/partially contains Downscaling Probablistic(Bayesian) Perspectives Link to Data Assimilation Example: NAM-SCA

36 Subgrid-Scale Information Useful for Downscaling Contained in Parameterization cloud fraction convective precipitation rate convective mass-flux = convection fraction x convective vertical velocity subgrid-scale distribution of water subgrid-scale vertical (heat) transport etc

37 Needs For More Coordinated Downscaling-Parameterization Studies

38 Conclusions Limitations of Traditional Approaches: Parameterization: No Interactions between the subgrid-scale elments: No Geometrical Information Downscaling: No Physics (statistical) or Off-Line (regionalization)

39 Conclusions Subgrid-Scale Representation (SSR): Downscaling Parameterization Multiresolutional Analysis: A Systematic Approach: Mode Decomposition: Compression & Decompression Example of SSR: NAM-SCA: Nonhydrostatic Anelastic Model with Segmentally-Constnat Appoximation: decomposition by ensemble of plumes Limitations of Traditional Approaches: