Subgrid-Scale Transport in Subgrid-Scale Transport in Cloud-Resolving ModelsCloud-Resolving Models

Chin-Hoh MoengNCAR Earth System Lab

& CMMAP

NCAR & CMMAP are sponsored by the National Science Foundation

IPAM workshop (May 2010)

OUTLINEOUTLINE

1. SGS processes in climate models1. SGS processes in climate models

2. Database (Giga-LES) and approach2. Database (Giga-LES) and approach

3. 3. A priori A priori test of a two-part SGS schemetest of a two-part SGS scheme

• governed by different equations • applied to different scales • used by different groups of researchers

GCM scales (resolvable)

microphysics; radiation; land-processes

shallow st/cu

cld-scale interactions missing in most GCMs.

deep convection PBL turbulence

SGS in conventional SGS in conventional GCMsGCMs

SGS processes---represented separatelySGS processes---represented separately

• cloud/precip. PBL turbulencecloud/precip. PBL turbulence• cloud/precip. land process cloud/precip. land process • cloud dynamics microphysicscloud dynamics microphysics• cloud dynamics mass transportcloud dynamics mass transport• cloud amount radiationcloud amount radiation• … …..

As computer power grows, global As computer power grows, global

models models

are using finer grid:are using finer grid:

Fine-grid NWP Fine-grid NWP

Global Cloud Resolving Model (GCRM) Global Cloud Resolving Model (GCRM)

to explicitly calculate large cloud to explicitly calculate large cloud

systems.systems.

Fine-grid NWP or GCRMFine-grid NWP or GCRM

Unified GCM-CRM dynamics

Conventional GCM grid ~ O(100 km)Conventional GCM grid ~ O(100 km)

CRM grid ~ several CRM grid ~ several kmskms

SGSSGSin CRMsin CRMs

SGS processes in CRMs:SGS processes in CRMs:• small and thin clouds small and thin clouds (PBL stratocumulus and fair-weather cu)(PBL stratocumulus and fair-weather cu)

• transport by small conv. & turbulencetransport by small conv. & turbulence• cloud microphysicscloud microphysics• radiative transferradiative transfer• land processesland processes• … …

turbulent turbulent motionsmotions

small, shallow cloudssmall, shallow clouds

They transport heat, moisture,…They transport heat, moisture,…& are crucial to cloud system development. & are crucial to cloud system development.

Within a deep cloud Within a deep cloud system, there are:system, there are:

To improve representation of To improve representation of

SGS transport in CRMs.SGS transport in CRMs.

Objective:

OUTLINEOUTLINE

1.1. SGS processes in climate modelsSGS processes in climate models

2. Database (Giga-LES) and 2. Database (Giga-LES) and

approachapproach

3. 3. A priori A priori test of a two-part SGS test of a two-part SGS

schemescheme

Benchmark simulation: Benchmark simulation: Giga-LESGiga-LES

• Grid points: 2048 x 2048 x 256Grid points: 2048 x 2048 x 256• Domain: 204.8 km x 204.8 km x 27 kmDomain: 204.8 km x 204.8 km x 27 km• Grid size: dx = dy = 100 m; dz = 50 m ~ 150 Grid size: dx = dy = 100 m; dz = 50 m ~ 150

mm• Performed by Marat KhairoutdinovPerformed by Marat Khairoutdinov• Code: SAM (Marat’s LES/CRM code)Code: SAM (Marat’s LES/CRM code)• Computer: Brookhaven’s BlueGeneComputer: Brookhaven’s BlueGene• Idealized GATE sounding & steady LS forcingIdealized GATE sounding & steady LS forcing• Time integration: 24 hrs (including spin-up)Time integration: 24 hrs (including spin-up)• Total 4D data ~ 5.5 TB (available to public)Total 4D data ~ 5.5 TB (available to public)

Use a unified CRM-LES code.Use a unified CRM-LES code.

Numerical database: Giga-Numerical database: Giga-LESLES

Cloud Resolving ModelCloud Resolving Model(CRM)(CRM)

Large Eddy SimulationLarge Eddy Simulation(LES)(LES)

deep convection systemdeep convection system PBL turb./shallow cloudPBL turb./shallow cloudanelastic dynamicsanelastic dynamicsice microphysicsice microphysics

(typically) Boussinesq(typically) Boussinesqwarm rainwarm rain

SGS just small turb eddiesSGS just small turb eddiesSGS includes all turb. SGS includes all turb.

100 km 10 km 100 m1 km 10 m

Unified dynamics for both scales Unified dynamics for both scales (e.g., SAM) (e.g., SAM) Giga-LES Giga-LES

Computer-generated cloud field:

from Marat Khairoutdinov205 km (~ a GCM grid cell)

N A typical

LES domain

On the other hand….On the other hand….

~ Giga-LES domain size

resolves convection system, resolves convection system, large & small convection and large & small convection and

turbulence…turbulence…

The benchmark The benchmark simulation:simulation:

To learn how To learn how small conv. & turbulencesmall conv. & turbulence respond to respond to deep (large) convectiondeep (large) convection..

… … to express to express SGS fluxesSGS fluxes in terms of in terms of CRM-resolved flow fieldCRM-resolved flow field..

Spectra and co-spectrum of w and q Spectra and co-spectrum of w and q

1. no spectral gap 1. no spectral gap near CRM gridnear CRM grid

2. energy peak 2. energy peak near CRM gridnear CRM grid

3. lots of q-flux by3. lots of q-flux by motions belowmotions below CRM gridCRM grid

z ~1 km

z ~1 km

z ~1 km

z ~5 km

z ~5 km

z ~5 km

w-spectra

q-spectra

wq-cospectra

typical CRM grid

intointo large conv. large conv. & & small conv./turbulencesmall conv./turbulence

Separate scales of Giga-LESSeparate scales of Giga-LES

Split the Giga-LES field into:Split the Giga-LES field into:CRM-resolvable CRM-resolvable && CRM-SGS CRM-SGS using a smooth low-pass filter.

100 km100 km 10 km10 km 1 km1 km 100 m100 m

These are scales resolved in giga-LES.These are scales resolved in giga-LES.

Apply a Gaussian filter with a filter width of 4 km Apply a Gaussian filter with a filter width of 4 km

FS: CRM resolvable FS: CRM resolvable

FSFSSFS(w-var)SFS(w-var) SFS: CRM-SGSSFS: CRM-SGS

SFS (wq-cov)SFS (wq-cov)

FSFS

FSFS

SFS(q-var)SFS(q-var)

1. most of w-variance in SFS1. most of w-variance in SFS

2. about half of q-flx in SFS2. about half of q-flx in SFS

Horizontal distributions of q-Horizontal distributions of q-fluxesfluxes

before & after filteringbefore & after filteringbenchmark q-fluxbenchmark q-flux

SFS fluxSFS flux CRM resolvable fluxCRM resolvable flux

at z=200mat z=200m

wq−wq

wq

wq

wq

-700~1500 W/m2

-5000~15000 W/m2

The SFS fluxesThe SFS fluxes

The L term represents the largest SFS The L term represents the largest SFS eddies.eddies.

τwc ≡ wc − wc

L =wc −wc

C =wc'+ w'c −wc'−w'c

R =w'c'−w'c'

further decompose:

Germano 1986; Leonard 1974

(Leonard term)

(Cross term)

(Reynolds term)

L-termL-term

R-termR-termC-termC-term

τwq

total SFS q-flx

SFS-wq components retrieved from Giga-LESSFS-wq components retrieved from Giga-LES

filter width=4 km

at z~ 5 km

-300 ~ 20000 W/m2 -100 ~ 4000 W/m2

-1000 ~ 5000 W/m2 -200 ~ 16000 W/m2

Approximation for the L termApproximation for the L term

w ≈w+Δ f

2

24[∂2w∂x∂x

+∂2w∂y∂y

] + ....use Taylor series:

L ≡wc −wc ≈(Δ f

2

12)[

∂w∂x

∂c∂x

+∂w∂y

∂c∂y

]

following Leonard (1974) and Clark et al (1979)following Leonard (1974) and Clark et al (1979)

It is a good approximation withno closure assumption.

Correlation coefficient between the benchmark L term and the approximation, for filter widths of 4 & 10 km.

The two-part scheme for The two-part scheme for SGS fluxes in CRMsSGS fluxes in CRMs

τwc = −Kh∂c

∂z+ 2(

Δ f

12

2

)[∂w

∂x

∂c

∂x+∂w

∂y

∂c

∂y]

w& c are CRM resolvable variables.where

The Giga-LES suggests that C ~ L.

τwc = −Kh∂c

∂z+ 2(

Δ f

12

2

)[∂w

∂x

∂c

∂x+∂w

∂y

∂c

∂y]

First part is the commonly used Smag.-Deardorff SGS model needed for energy dissipation.

Second part is the L+C term, for scale interaction; it is easy to implement in CRMs.

OUTLINEOUTLINE

1.1. SGS processes in climate modelsSGS processes in climate models

2. Database (Giga-LES) and approach2. Database (Giga-LES) and approach

3. 3. A priori A priori test of the two-part SGS schemetest of the two-part SGS scheme

from old K-schemefrom old K-scheme from LES (“truth”)from LES (“truth”) from the 2-part schemefrom the 2-part scheme

x (km)x (km)

y(k

m)

y(k

m)

Horizontal distributions of Horizontal distributions of vertical q-fluxvertical q-flux at z ~ 1.5 km at z ~ 1.5 km

A prioriA priori test of the SGS test of the SGS scheme: scheme:

τwq

spatial correlation

A priori A priori test for SFS wq test for SFS wq

Spatial correlation coefficientsSpatial correlation coefficientswith the LES-retrieved SFS-wq with the LES-retrieved SFS-wq

Contributions to the horizontallyContributions to the horizontallyaveraged SFS-wqaveraged SFS-wq

deep c

ld

deep c

ld

layer

layer

solid curves: filter width = 4 kmdotted curves: filter width = 10 km

A priori A priori test for SFS uq test for SFS uq

Spatial correlation coefficientsSpatial correlation coefficientswith the LES-retrieved SFS-uqwith the LES-retrieved SFS-uq

Contributions to the horizontallyContributions to the horizontallyaveraged SFS-uqaveraged SFS-uq

A priori A priori test for SFS uwtest for SFS uw

Spatial correlation coefficientsSpatial correlation coefficientswith the LES-retrieved SFS-uwwith the LES-retrieved SFS-uw

Contributions to the horizontallyContributions to the horizontallyaveraged SFS-uwaveraged SFS-uw

solid curves: 4 kmdotted curves: 10 km

SUMMARYSUMMARY

• Giga-LES is useful benchmark to study SGS for CRMs.Giga-LES is useful benchmark to study SGS for CRMs.

• No spectral gap exists between CRM-resolvable & No spectral gap exists between CRM-resolvable &

SGS.SGS.

• Most energy & transport occur near typical CRM grid,Most energy & transport occur near typical CRM grid,

thus largest SGS eddies are important.thus largest SGS eddies are important.

• A prior A prior test of the two-part SGS transport scheme test of the two-part SGS transport scheme shows promising results. Full test next…shows promising results. Full test next…

NCAR is sponsored by the National Science Foundation