Training course: boundary layer IV Parametrization above the surface layer (layout) Overview of...
-
Upload
joselyn-stile -
Category
Documents
-
view
219 -
download
0
Transcript of Training course: boundary layer IV Parametrization above the surface layer (layout) Overview of...
training course: boundary layer IV
Parametrization above the surface layer (layout)
• Overview of models
• Slab (integral) models
• K-closure model
• K-profile closure
• tke closure
training course: boundary layer IV
Parametrization above the surface layer (layout)
• Overview of models
• Slab (integral) models
• K-closure model
• K-profile closure
• tke closure
training course: boundary layer IV
Parametrization above the surface layer (overview)
Type of parametrization Application
Geostrophic drag laws Models with very low vertical resolution (used very little)
Slab (integral) models Models that treat top of the boundary as surface
Inversion restoring methods Method to enhance resolution near inversions
K-closure Models with fair resolution
K-profile closure Models with fair resolution
TKE-closure Models with high resolution
training course: boundary layer IV
Parametrization above the surface layer (layout)
• Overview of models
• Slab (integral) models
• K-closure model
• K-profile closure
• tke closure
training course: boundary layer IV
Integral models
Integral models can be formally obtained by:
•Making similarity assumption about shape of profile, e.g.
•Integrate equations from
•Solve rate equations for scaling parameters
*( ) / ( / )G f z h
0z to z h
*, ,G and h
Mixed layer model of the day-time boundary layer is a well-known example of integral model.
training course: boundary layer IV
Mixed layer (slab) model of day time BL
( ' ') ( ' ')om
h
dw
dth w
ow )''(
z z
hw )''( hz
z
m
me
dh
dtw
m mew
d d
dt dt
( ' ')h e mw w
This set of equations is not closed. A closure assumption is needed for entrainment velocity or for entrainment flux.
training course: boundary layer IV
Closure for mixed layer model
Closure is based on kinetic energy budget of the mixed layer:
Buoyancy flux in inversion scales with production in mixed layer:
3*( ' ') ( ' ')h E o S
ug gw C w C
h
CE is entrainment constant (0.2)Cs represents shear effects (2.5-5) but is often not considered
training course: boundary layer IV
Parametrization above the surface layer (layout)
• Overview of models
• Slab (integral) models
• K-closure model
• K-profile closure
• tke closure
training course: boundary layer IV
Grid point models with K-closure
qTVU ,,,
oz
33
150
356
640
970
1360
1800
oz
10
30
60
90
140
190
260
qTVU ,,,
qTVU ,,,
qTVU ,,,
qTVU ,,,
qTVU ,,,
qTVU ,,,
ss qT ,,0,0
qTVU ,,,
qTVU ,,,
2300
2800
330
420
91-levelmodel
31-levelmodel
Levels in ECMWF modelK-diffusion in analogy with molecular diffusion, but
Diffusion coefficients need to be specified as a function of flow characteristics (e.g. shear, stability,length scales).
z
qKwq
zKw
z
VKwv
z
UKwu
HH
MM
'',''
'',''
training course: boundary layer IV
Diffusion coefficients according to MO-similarity
,,2
2
2
dZ
dUK
dZ
dUK
hmH
mM
,111
z m150
z
2.0
m2000
z
222*
*2|/|
/
m
h
m
h
v
v
v Lu
g
dzdU
dzdgRi
Use relation between and
to solve for
L/
L/
Ri
training course: boundary layer IV
Louis formulation
,,2
2
2
dZ
dUK
dZ
dUK
hmH
mM
is equivalent to
,, 22
dZ
dUFK
dZ
dUFK HHMM
with )(),( RiFFRiFF HHMM
The Louis formulation specifies empirical functions of the Ri-number, whereas the MO-formulation specifies empirical functions of z/L. The two formulations are compatible in principle because:
12 )(, hmHmM FF
training course: boundary layer IV
Stability functions
FM,H based on Louis are very different from observational based (MO) (universal) functions. Louis’ functions provided larger exchanges for stable layers
unstable
stable
training course: boundary layer IV
Geostrophic drag law derived from single column simulations. Observations are from Wangara experiment.
Geostrophic drag law
MO-based FM,H give more realistic drag law, with less friction (A) and a larger ageostrophic angle (B)
More drag
Larger ageos. angle
training course: boundary layer IV
Single column simulations of stable BL
Fm
Fh
LTG
Revised LTGMO
Revised LTG
LTGMO
Three different forms of stability functions:
1. Derived from Monin Obukhov functions (based on observations)
2. Louis-Tiedtke-Geleyn (empirical Ri-functions)
3. Revised LTG with more diffusion for heat and less for momentum.
training course: boundary layer IV
Stable BL diffusion
Revised LTG has been designed to have more diffusion for heat, without changing the momentum budget
Near surface cooling is sensitive to strength of FH
20 25H Wm
20 25H Wm
20 25H Wm
w
w u
250 WmHo
training course: boundary layer IV
Stable BL diffusion
Relaxation integration Jan 96; 2m T-diff.: Revised LTG - control
training course: boundary layer IV
K-closure with local stability dependence (summary)
• Scheme is simple and easy to implement.
• Fully consistent with local scaling for stable boundary layer.
• Realistic mixed layers are simulated (i.e. K is large enough to create a well mixed layer).
• A sufficient number of levels is needed to resolve the BL i.e. to locate inversion.
• Entrainment at the top of the boundary layer is not represented (only encroachment)!
flux
training course: boundary layer IV
Parametrization above the surface layer (layout)
• Overview of models
• Slab (integral) models
• K-closure model
• K-profile closure
• tke closure
training course: boundary layer IV
K-profile closure Troen and Mahrt (1986)
Heat flux
h
hK
z
}{''
z
Kw H
3/13*1
3* }{ wCuws
2)/1( hzzkwK sh Profile of diffusion coefficients:
hwwC so /)''(
Find inversion by parcel lifting with T-excess: sovsvs wwd /)''(,
such that: 25.02222
sshh
vsvh
vc VUVU
ghRi
See also Vogelezang and Holtslag (1996, BLM, 81, 245-269) for the BL-height formulation.
training course: boundary layer IV
K-profile closure (ECMWF implementation)
Moisture flux
Entrainment fluxes
Heat flux
zi
q
ECMWF entrainment formulation:
Eiv
ovhi C
z
wK
)/(
)''(
ECMWF Troen/MahrtC1 0.6 0.6
D 2.0 6.5
CE 0.2 -
Inversion interaction was too aggressive in original scheme and too much dependent on vertical resolution. Features of ECMWF implementation:
•No counter gradient terms.•Not used for stable boundary layer.•Lifting from minimum virtual T.•Different constants.•Implicit entrainment formulation.
training course: boundary layer IV
Mixed layer parametrization
Heat flux
Mixed layer after 9 hours of heating from the surface by 100 W/m2 with 3 different parametrizations.
Potential temperature
1 2Km/(kzu*)0
Diffusion coefficientsProfiles of:
training course: boundary layer IV
Mixed layer parametrization
Day time evolution of BL height from short range forecasts(composite of 9 dry days in August 1987 during FIFE)
training course: boundary layer IV
Mixed layer parametrization
Day time evolution of BL moisture from short range forecasts(composite of 9 dry days in August 1987 during FIFE)
OBS
K-profile
Louis-scheme
training course: boundary layer IV
Diurnal cycle over land
Combination of drying from entrainment and surface moistening gives a very small diurnal cycle for q
training course: boundary layer IV
K-profile closure (summary)
• Scheme is simple and easy to implement.
• Numerically robust.
• Scheme simulates realistic mixed layers.
• Counter-gradient effects can be included (might create numerical problems).
• Entrainment can be controlled rather easily.
• A sufficient number of levels is needed to resolve BL e.g. to locate inversion.
training course: boundary layer IV
Parametrization above the surface layer (layout)
• Overview of models
• Slab (integral) models
• K-closure model
• K-profile closure
• tke closure
training course: boundary layer IV
TKE closure
z
qKwq
zKw
z
VKwv
z
UKwu
HH
MM
'',''
'',''
Eddy diffusivity approach:
With diffusion coefficients related to kinetic energy:
MHHKKM KKECK ,2/1
training course: boundary layer IV
Closure of TKE equation
' '' ' ' ' ' ' ( ' ' )
o
E U V g p wu w v w w E w
t z z z
TKE from prognostic equation:
z
EK
wpwE
EC E
)''
''(,2/3
with closure:
Main problem is specification of length scales, which are usually a blend of , an asymptotic length scale and a stability related length scale in stable situations.
z
training course: boundary layer IV
TKE (summary)qTVU ,,,
qTVU ,,,
qTVU ,,,
ss qT ,,0,0E
E
E
•TKE has natural way of representing entrainment.•TKE needs more resolution than first order schemes.•TKE does not necessarily reproduce MO-similarity.•Stable boundary layer may be a problem.
Best to implement TKE on half levels.