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Budgets of second order moments for cloudy boundary layers derived from LES. 5 September 2011 Rieke Heinze , Siegfried Raasch Institute for Meteorology und Climatology Leibniz University Hannover, Germany Dmitrii Mironov German Weather Service. - PowerPoint PPT Presentation
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Budgets of second order moments for cloudy boundary layers 1Systematische Untersuchung höherer statistischer Momente und ihrer Bilanzen 1LES der atmosphärischen Grenzschichtturbulenz –systematische Untersuchung höherer statistischer Momente und ihrer Bilanzen
5 September 2011
Rieke Heinze, Siegfried RaaschInstitute for Meteorology und Climatology
Leibniz University Hannover, Germany
Dmitrii MironovGerman Weather Service
Budgets of second order moments for cloudy boundary
layers derived from LES
COSMO General Meeting, Rome, September 2011
Budgets of second order moments for cloudy boundary layers 2
Background (I)
• Atmospheric boundary layer is characterized by turbulent motions
• In weather prediction and climate models turbulence and shallow convection have to be parameterized
• A lot of closure models are based on the truncated ensemble-mean budget equations for the statistical moments of second order:
...
...2
li
l
ut
t
...
...2
1 2
ji
i
uut
ut
...
...2
qut
qt
i
...
lqt
Motivation LES Results Summary Outlook
Budgets of second order moments for cloudy boundary layers 3
Background (II)
• Budgets are needed for– Estimation of relative importance of the budget terms– Testing of parameterizations and further development– Determination of disposable/tuning parameters
Budgets have a fundamental meaning So far: lack of systematic and comprehensive analysis for cloudy
boundary layers Usage of large eddy simulation (LES) to determine all the budgets
of second order moments and to examine pressure correlation terms like
ix
pq
il x
p
or
Motivation LES Results Summary Outlook
Budgets of second order moments for cloudy boundary layers 44
x
z
k
E | Production | Inertial subrange | Dissipation |
Introduction• Scales of turbulence
– Large eddies: 103 m, 1 h– Small eddies: 10-3 m, 0.1 s
• Spectrum of TKE– Large scales: production– Small scales: dissipation
• Filtering– Large, energy containing
eddies are resolved – Small eddies are modeled
Calculation of a turbulent boundary layer flow
LES: volume average
/1
Resolved scale
Subgridscale
Motivation LES Results Summary Outlook
Budgets of second order moments for cloudy boundary layers 5
Budgets from LES
• Closure models are often based on ensemble-mean budgets
• LES: approximation by averaging over horizontal planes and afterwards over several time steps
• LES is based on filtering: Application to budget equations as well:
Explicit consideration of SGS budgets
Motivation LES Results Summary Outlook
ttt
Budgets of second order moments for cloudy boundary layers 6
mixed layer
cloud layer
inversion
BOMEX − first order moments
• BOMEX LES study (Siebesma et al., 2003, 10 LES models, GCSS)– Stationary case of shallow cumulus convection over ocean (no precip.)– Domain size: 6.4 x 6.4 x 3.0km3, grid spacing: Δ=10m, time: 6h
Motivation LES Results Summary Outlook
Budgets of second order moments for cloudy boundary layers 7
BOMEX − TKE and its budget
Motivation LES Results Summary Outlook
Budgets of second order moments for cloudy boundary layers 8
BOMEX − temperature variance and its budget
Motivation LES Results Summary Outlook
Budgets of second order moments for cloudy boundary layers 9
BOMEX − variance of total water content and its budget
Motivation LES Results Summary Outlook
Budgets of second order moments for cloudy boundary layers 10
BOMEX − temperature flux and its budget
Motivation LES Results Summary Outlook
Budgets of second order moments for cloudy boundary layers 11
DYCOMS − first results
• DYCOMS LES study (Stevens et al., 2005, 10 LES models, 16 sim.)– Homogeneous, nocturnal stratocumulus over ocean (no drizzle)– Domain size: 3.4 x 3.4 x 1.5km3, grid spacing: Δ=35m, Δz=5m, time: 4h
Motivation LES Results Summary Outlook
Budgets of second order moments for cloudy boundary layers 12
Summary
• Budgets for all second order moments (16 equations) for cloud topped boundary layers are determined with very high resolution LES (2560 x 2560 x 1280 grid points)
• PALM is able to simulate GCSS cases
• Shallow cumulus (BOMEX)– Budgets of
• TKE and scalar variances: production and dissipation largest but transport is also very important
• Scalar fluxes: importance of buoyancy and pressure scalar cov.
• Stratocumulus (DYCOMS)– First results look promising
Motivation LES Results Summary Outlook
Budgets of second order moments for cloudy boundary layers 13
Future plans
• Simulation of a SC-CU transition case
• Detailed examination of pressure-scalar and -velocity covariance
• Testing of existing parameterizations against LES data
• LES data set will be made available – Testing and evaluation of currently used closure schemes– Further development of new schemes (→ e.g. TKE-scalar variance
scheme)
• Data is in netCDF format and preparation of a detailed documentation is ongoing
Motivation LES Results Summary Outlook
Benefit for COSMO community
Budgets of second order moments for cloudy boundary layers 14
Supplementary material
Budgets of second order moments for cloudy boundary layers 15Systematische Untersuchung höherer statistischer Momente und ihrer Bilanzen 1515
LES basic equations (I) • Filtering: with
• Basic system of equations consists of the filtered Navier-Stokes equations in Boussinesq form
Volume balance approach (Schumann, 1975)
VdtVzyx
tVV
,1
,
j
rij
vigkikjijkij
iji
x
gufuf
xx
uu
t
uk
*
0333
*
0
1
Equations of motion
ijjirij euu
3
2
2
2
1iue
ep 0**
3
2 Modified pressure
SGS stress
SGS TKE 0
j
j
x
uContinuity equation
Budgets of second order moments for cloudy boundary layers 16
Conservation equation
PRECj
qj
j
j
t
q
xx
qu
t
q
1616
LES basic equations (II)• Filtering: with
• Basic system of equations consists of the filtered Navier-Stokes equations in Boussinesq form
Volume balance approach (Schumann, 1975)
VdtVzyx
tVV
,1
,
First principle
PREC
l
RAD
l
j
j
j
ljl
ttxx
u
t
Potential liquid water temperature:
ljj u
lp
vl q
Tc
L
SGS temperature flux:
Total water contentlv qqq
qu jqj SGS humidity flux
Budgets of second order moments for cloudy boundary layers 171717
LES SGS turbulence parameterization (I)• Turbulence closure based on Deardorff,1980
– Flux-gradient relationship for SGS fluxes– Prognostic equation for SGS TKE
• Diffusion coefficients
• The mixing length depends on– Grid spacing– Distance to nearest solid wall– Stratification
e
i
j
j
im
rij x
u
x
uK
j
lhj x
K
jhqj x
qK
elcK mm mh Kl
K )2
1(
3/1)( zyx mitund
l
02,,7.0min
02,7.0min
Nsld
Nd
ld
N
Budgets of second order moments for cloudy boundary layers 18
03
0
peu
xu
g
x
uuu
x
eu
t
ej
jv
j
iji
j
j
• The prognostic equation for ise
1818
LES SGS turbulence parameterization (II)• Turbulence closure based on Deardorff,1980
– Flux-gradient relationship for SGS fluxes– Prognostic equation for SGS TKE
• Diffusion coefficients
e
i
j
j
im
rij x
u
x
uK
j
lhj x
K
jhqj x
qK
elcK mm mh Kl
K )2
1(
3/1)( zyx mitund
Budgets of second order moments for cloudy boundary layers 19
BOMEX − second order moments
Buoyancy flux Total water flux
Budgets of second order moments for cloudy boundary layers 20
BOMEX − skewness
Cumulus convection shows strong updrafts of moist and cold air within cloud layer
2/32
3
S
(important for e.g. statistical cloud schemes)
Budgets of second order moments for cloudy boundary layers 21
BOMEX − covariance and its budget
Budgets of second order moments for cloudy boundary layers 22
BOMEX − flux of total water content and its budget