1. Parametrization of turbulent fluxes in the outer layer Irina Sandu
Overview of models
Bulk models
Local K-closure
K-profile closure
ED/MF closure
TKE closure
Current closure in the ECMWF model
0 order
1st order
non-local
1.5th order

2. Reynolds equations
Reynolds Terms

3. Parametrization of turbulent fluxes in the outer layer
Overview of models
Bulk models
Local K closure
K-profile closure
ED/MF closure
TKE closure
Current closure in the ECMWF model

4. Local K closure Levels in ECMWF model
K-diffusion in analogy with molecular diffusion, but
137-level
model
Diffusion coefficients need to be specified as a function of flow characteristics (e.g. shear, stability,length scales).

5. Diffusion coefficients according to MO-similarity
Use relation between and
to solve for

6. Stable boundary layer in the IFS: closure and caveats
f(Ri)
Long tails
Short tails MO
1/l=1/kz+1/λ
Long tails
Recent years (36R4 – 38R2)
Surface layer – Monin Obukhov
Above: f = α* fLT + (1- α) * fST
α = exp(-H/150)
λ=150m
short tails
Long tails
Short tails MO
As in other NWP models the diffusion maintained in stable conditions is stronger than what LES or observations indicate
Long tails
short tails

7. Stable boundary layer in the IFS: closure and caveats
Wind turning is underestimated
Mean nocturnal bias over Europe
2m T is too low despite too strong diffusion
obs
200m
Mean annual wind speed at Cabaw
model
The strong diffusion maintained in stable conditions in the ECMWF model inherently translates in the type of biases pointed out in the GABLS framework. In the top plot you can see in red the bias in wind direction at the surface with respect to observations from 1992 to As you can see if this bias varied slightly along the years due to changes in the model, it always indicates an underestimation of the wind turning in the boundary layer, and this underestimation is even in recent years if approx. 10 degrees. The two plots below show the modeled and observed wind speed at 10, 80 and 200m at Cabauw for 1987 and 2011, from ERA-40 and OP. Again you can see that despite the model improvements between era-40 and the 2011 model, the low level jet is still underestimated at nighttime while the wind at the surface is slightly overestimated, which points again to a too strong mixing in stable PBL.
80 m
10 m
2011 OPERATIONAL
Time (UTC)

8. Impact of reducing the diffusion in stable conditions
ST: long tails short tails
LT30: λ=150m λ=30m
1/l=1/kz+1/λ , λ=150m
Almost halves the errors in low level jet, also increases the wind turning

9. + Increase in drag over orography
Stable boundary layer : changes to closure in 40R1 (Nov. 2013)
Turbulence closure for stable conditions:
Up to 38R2
long tails near surface, short tails above PBL
λ =150m
non-resolved shear term, with a
maximum at 850hPa
From 40R1
long tails everywhere
λ = 10% PBL height in stable boundary layers
λ = 30 m in free shear layers +
Increase in drag over orography
Increase in atm/surf coupling
As in the past years, the bulk of the boundary layer activities focused on improving the representation of stable boundary layers. Just for reminder, as most of global NWP we are using too much diffusion in stable conditions, which leads to biases in key features of stable boundary layers, notably the near-surface winds. Building on the extensive study we did to investigate whether is possible to reduce the diffusion in stable conditions, summarized in a paper that came up this year, we came up with a solution which allows to reduce the diffusion and to improve the near-surface winds. This changes leads to a net red……In order to compensate the negative effects on the large-scale perf and the 2m temp of the changes to the turb closure, we combined them with an ….
Consequence: net reduction in diffusion in stable boundary layers, not much change in free-shear layers, except at 850 hPa
ECMWF Newsletter, no 138

10. Stable boundary layer : changes to closure in 40R1 (Nov. 2013)
small changes in 2m temperature during nigh time in winter (~0.1 K over Europe)
Reduction of wind direction bias over Europe by 3 in winter, 1  in summer (out of 10 )
Improvement in low level jets (next slide)
Improvement of the large-scale performance of the model in winter N.Hemisphere
Deterioration of tropical wind scores (against own analysis, not against observations)

11. Improvement of low level winds
Cabauw
Comparison with tower data
T511L137 analysis runs
JJA 2012, 0 UTC, step 24h
Hamburg
Improvement in both mean and RMSE in the upper part of stable boundary layers
Falkenberg

12. K-closure with local stability dependence (summary)
Scheme is simple and easy to implement.
Fully consistent with local scaling for stable boundary 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

13. Parametrization of turbulent fluxes in the outer layer
Overview of models
Bulk models
Local K-closure
K-profile closure
ED/MF closure
TKE closure
Current closure in the ECMWF model

14. K-profile closure Troen and Mahrt (1986)
Heat flux h
Profile of diffusion coefficients:
Find inversion by parcel lifting with T-excess:
Ri_c=0.25 is irrelevant for a mixed layer (any number will do). For stable layers, it gives a realistic result
such that:

15. 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.

16. Parametrization of turbulent fluxes in the outer layer
Overview of models
Bulk models
Local K closure
K-profile closure
ED/MF closure
TKE closure
Current closure in the ECMWF model

17. K-diffusion versus Mass flux method
K-diffusion method - used to describe the small-scale turbulent motions:
analogy to
molecular diffusion
Mass-flux method – used to describe the strong large-scale updraughts:
mass flux
entraining plume model
detrainment rate

18. ED/MF framework a (neglected)
The updraught: small fractional area a, containing the strongest upward vertical motions a
sub-core flux
env. flux
M-flux
(neglected)
Siebesma & Cuijpers, 1995

19. BOMEX LES decomposition
M-flux
sub-core flux
total flux
env. flux
M-flux covers 80% of flux
Siebesma & Cuijpers, 1995

20. Parametrization of turbulent fluxes in the outer layer
Overview of models
Bulk models
Local K closure
K-profile closure
ED/MF closure
TKE closure
Current closure in the ECMWF model

21. TKE closure (1.5 order)
Eddy diffusivity approach:
With diffusion coefficients related to kinetic energy:

22. Closure of TKE equation
Pressure correlation
TKE from prognostic equation:
Storage
Shear production
Buoyancy
Turbulent
transport
Dissipation
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.

23. TKE (summary) 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.

24. Parametrization of turbulent fluxes in the outer layer
Overview of models
Bulk models
Local K closure
ED/MF closure
K-profile closure
TKE closure
Current closure in the ECMWF model

25. Current turbulence closure in the ECMWF model
Stable surface layer
Unstable surface layer
K-diffusion closure
(f(Ri) for stable/unstable layers)
K-diffusion closure
(f(Ri) for stable/unstable layers)
ED/MF
(K-profile + M flux)
PBL_TYPE=0
PBL_TYPE=1,2,3

26. Unstable surface layer : ED/MF approach in the PBLK
Shallow cumulus
Deep cumulus
Stratocumulus
dry BL
zcb zi
Kbot
Zi=W<0
Kentr
Zi=Zcb
Kprof+
Ktop
Kprof
Mixed layer
Kprof K
PBL_TYPE=1
PBL_TYPE=2
PBL_TYPE=3
EIS>7
EIS<7
Parcel method:
If no cloud base
IF cloud base

27. Caveats and challenges
If stratocumulus (PBL_TYPE=2)
no shallow convection
Extra Kdiff due to cloud top radiative cooling
mixing in thetal, qt, then qc computed with simple pdf scheme, and given to cloud scheme
only scheme which gives explicitly dqc to cloud scheme
If decoupled (PBL_TYPE=3)
No top entrainment
No mass flux from PBL
PBL parcel different from shallow convection parcel
Handling of stratocumulus to cumulus transitions
Ongoing work towards a more unified treatment of diffusion, shallow convection and cloud