Transcript clws3 9181

Subgrid-Scale Transport in
Cloud-Resolving Models
Chin-Hoh Moeng
NCAR Earth System Lab
& CMMAP
IPAM workshop (May 2010)
NCAR & CMMAP are sponsored by the National Science Foundation
OUTLINE
1. SGS processes in climate models
2. Database (Giga-LES) and approach
3. A priori test of a two-part SGS scheme
• governed by different equations
• applied to different scales
• used by different groups of researchers
SGS in conventional GCMs
GCM scales
(resolvable)
PBL
turbulence
deep convection
shallow st/cu
microphysics; radiation; land-processes
SGS processes---represented separately
cld-scale interactions missing in most GCMs.
However, cloud-scale interactions
are many and crucial:
• cloud/precip.
• cloud/precip.
• cloud dynamics
• cloud dynamics
• cloud amount
• ….
PBL turbulence
land process
microphysics
mass transport
radiation
As computer power grows, global models
are using finer grid:
 Fine-grid NWP
 Global Cloud Resolving Model (GCRM)
to explicitly calculate large cloud systems.
Fine-grid NWP or GCRM
Unified GCM-CRM dynamics
Conventional GCM grid ~ O(100 km)
CRM grid ~ several kms
SGS
in CRMs
SGS processes in CRMs:
• small and thin clouds
(PBL stratocumulus and fair-weather cu)
•
•
•
•
•
transport by small conv. & turbulence
cloud microphysics
radiative transfer
land processes
…
Within a deep cloud system,
there are:
turbulent
motions
small, shallow clouds
They transport heat, moisture,…
& are crucial to cloud system development.
Objective:
To improve representation of
SGS transport in CRMs.
OUTLINE
1. SGS processes in climate models
2. Database (Giga-LES) and approach
3. A priori test of a two-part SGS scheme
Benchmark simulation:
Giga-LES
•
•
•
•
•
•
•
•
•
Grid points: 2048 x 2048 x 256
Domain: 204.8 km x 204.8 km x 27 km
Grid size: dx = dy = 100 m; dz = 50 m ~ 150 m
Performed by Marat Khairoutdinov
Code: SAM (Marat’s LES/CRM code)
Computer: Brookhaven’s BlueGene
Idealized GATE sounding & steady LS forcing
Time integration: 24 hrs (including spin-up)
Total 4D data ~ 5.5 TB (available to public)
Numerical database: Giga-LES
Use a unified CRM-LES code.
Cloud Resolving Model
(CRM)
100 km
10 km
deep convection system
anelastic dynamics
ice microphysics
SGS includes all turb.
Large Eddy Simulation
(LES)
1 km
100 m
PBL turb./shallow cloud
(typically) Boussinesq
warm rain
SGS just small turb eddies
Unified dynamics for both scales
(e.g., SAM)  Giga-LES
10 m
Computer-generated cloud field:
A typical
LES domain
N
205 km (~ a GCM grid cell)
from Marat Khairoutdinov
On the other hand….
~ Giga-LES
domain size
The benchmark simulation:
resolves convection system, large & small
convection and turbulence…
To learn how small conv. & turbulence
respond to deep (large) convection.
… to express SGS fluxes
in terms of CRM-resolved flow field.
Spectra and co-spectrum of w and q
typical CRM grid
1. no spectral gap
near CRM grid
w-spectra
z ~5 km
z ~1 km
2. energy peak
near CRM grid
q-spectra
z ~5 km
z ~1 km
wq-cospectra
z ~5 km
z ~1 km
3. lots of q-flux by
motions below
CRM grid
Separate scales of Giga-LES
into large conv. & small conv./turbulence
100 km
10 km
1 km
100 m
These are scales resolved in giga-LES.
Split the Giga-LES field into:
CRM-resolvable & CRM-SGS
using a smooth low-pass filter.
Apply a Gaussian filter with a filter width of 4 km
SFS(w-var)
FS
FS: CRM resolvable
SFS: CRM-SGS
SFS(q-var)
FS
1. most of w-variance in SFS
2. about half of q-flx in SFS
FS
SFS (wq-cov)
Horizontal distributions of q-fluxes
before & after filtering
benchmark q-flux
wq
 wq
-5000~15000 W/m2
SFS flux
wq  wq
CRM resolvable flux
wq
-700~1500 W/m2
at z=200m
The SFS fluxes
 wc  wc  wc
further
decompose:
L  wc  wc
(Leonard term)
C  wc'  w'c  wc'  w'c
R  w 'c'  w 'c'
(Cross term)
(Reynolds term)
Germano 1986; Leonard 1974
The L term represents the largest SFS eddies.
SFS-wq  wq components retrieved from Giga-LES
at z~ 5 km
total SFS q-flx
L-term
-300 ~ 20000 W/m2
-100 ~ 4000 W/m2
C-term
-1000 ~ 5000 W/m2
R-term
-200 ~ 16000 W/m2
filter width=4 km
Approximation for the L term
use Taylor series:
 f 2 2 w
2 w
ww
[

]  ....
24 xx yy
f
w c w c
L  wc  wc  (
)[

]
12 x x y y
2
following Leonard (1974) and Clark et al (1979)
It is a good approximation with
no closure assumption.
Correlation coefficient between the benchmark L term
and the approximation, for filter widths of 4 & 10 km.
The two-part scheme for
SGS fluxes in CRMs
The Giga-LES suggests that C ~ L.
 f w c w c
c
 K h
 2(
)[

]
z
12
x x y y
2
 wc
where w & c are CRM resolvable variables.
f
c
w c w c
 K h
 2(
)[

]
z
12
x x y y
2
 wc
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.
OUTLINE
1. SGS processes in climate models
2. Database (Giga-LES) and approach
3. A priori test of the two-part SGS scheme
A priori test of the SGS scheme:  wq
Horizontal distributions of vertical q-flux at z ~ 1.5 km
from LES (“truth”)
from the 2-part scheme
y(km)
from old K-scheme
x (km)
spatial correlation
deep cld layer
A priori test for SFS wq
Spatial correlation coefficients
with the LES-retrieved SFS-wq
solid curves: filter width = 4 km
dotted curves: filter width = 10 km
Contributions to the horizontally
averaged SFS-wq
A priori test for SFS uq
Spatial correlation coefficients
with the LES-retrieved SFS-uq
Contributions to the horizontally
averaged SFS-uq
A priori test for SFS uw
Spatial correlation coefficients
with the LES-retrieved SFS-uw
solid curves: 4 km
dotted curves: 10 km
Contributions to the horizontally
averaged SFS-uw
SUMMARY
• Giga-LES is useful benchmark to study SGS for CRMs.
• No spectral gap exists between CRM-resolvable & SGS.
• Most energy & transport occur near typical CRM grid,
thus largest SGS eddies are important.
• A prior test of the two-part SGS transport scheme
shows promising results. Full test next…
NCAR is sponsored by the National Science Foundation