Download presentation

Presentation is loading. Please wait.

Published byCarter Murray Modified over 4 years ago

1
**Parametrization of PBL outer layer Irina Sandu and Martin Kohler**

Overview of models Bulk models Local K-closure ED/MF closure K-profile closure TKE closure Current closure in the ECMWF model

2
Reynolds equations Reynolds Terms

3
**Parametrization of PBL outer layer (overview)**

Application Order and Type of Closure Bulk models Models that treat PBL top as surface 0th order non-local K-diffusion Models with fair resolution 1st order local Mass-flux 1st order non-local ED/MF (K& M) 1st order non-local K-profile TKE-closure Models with high resolution 1.5th order non-local Higher order closure 2nd or 3rd order non-local

4
**Parametrization of PBL outer layer**

Overview of models Bulk models Local K-closure ED/MF closure K-profile closure TKE closure Current closure in the ECMWF model

5
**Bulk - Slab - Integral - Mixed Layer Models**

Bulk models can be formally obtained by: Making similarity assumption about shape of profile, e.g. Integrate equations from z=0 to z=h Solve rate equations for scaling parameters , and h The mixed layer model of the day-time boundary layer is a well-known example of a bulk model.

6
**Mixed layer (bulk) model of day time BL**

energy mass inversion entrainment This set of equations is not closed. A closure assumption is needed for entrainment velocity or for entrainment flux.

7
**Closure for mixed layer model**

The closure is based on the turbulent kinetic energy budget of the mixed layer: Buoyancy flux in inversion scales with production in mixed layer: CE is entrainment constant (0.2) Cs represents shear effects (2.5-5) but is often not considered

8
**Parametrization of PBL outer layer**

Overview of models Bulk models Local K closure ED/MF closure K-profile closure TKE closure Current closure in the ECMWF model

9
**Local K closure Levels in ECMWF model**

K-diffusion in analogy with molecular diffusion, but 91-level model 31-level model Diffusion coefficients need to be specified as a function of flow characteristics (e.g. shear, stability,length scales).

10
**Diffusion coefficients according to MO-similarity**

Use relation between and to solve for

11
**Stable boundary layer in the IFS: current problems**

underestimation of T2m and of wind turning (low level jet poorly represented) Increase the vertical diffusion SFMO 1/l=1/kz+1/λ , λ=150m SFMO 36R4 Surface layer – SFMO Above: f = α* fLTG + (1- α) * fMO α = exp(-H/150)

12
**GABLS 3 . Impact of the stability functions**

U200m T2M U10m hours since 12 UTC hours since 12 UTC hours since 12 UTC

13
**GABLS 3 : Impact of the mixing length**

U200m T2M U10m hours since 12 UTC hours since 12 UTC hours since 12 UTC

14
**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 (only encroachment)! flux

15
**Parametrization of PBL outer layer**

Overview of models Bulk models Local K closure ED/MF closure K-profile closure TKE closure Current closure in the ECMWF model

16
**K-diffusion versus Mass flux method**

K-diffusion method: analogy to molecular diffusion Mass-flux method: mass flux entraining plume model detrainment rate

17
**M ED/MF framework a sub-core flux env. flux M-flux**

Siebesma & Cuijpers, 1995

18
**BOMEX LES decomposition**

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

19
**Parametrization of PBL outer layer**

Overview of models Bulk models Local K-closure ED/MF closure K-profile closure TKE closure Current closure in the ECMWF model

20
**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:

21
**K-profile closure (ECMWF up to 2005)**

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. Entrainment fluxes h Moisture flux Heat flux Original TM is too aggressive on inversions Entrainment is specified implicitly for stability. ECMWF entrainment formulation: ECMWF Troen/Mahrt C D CE

22
**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.

23
**Parametrization of PBL outer layer**

Overview of models Bulk models Local K closure ED/MF closure K-profile closure TKE closure Current closure in the ECMWF model

24
TKE closure (1.5 order) Eddy diffusivity approach: With diffusion coefficients related to kinetic energy:

25
**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.

26
**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.

27
**Parametrization of PBL outer layer**

Overview of models Bulk models Local K closure ED/MF closure K-profile closure TKE closure Current closure in the ECMWF model

28
**Current closure in the ECMWF model**

K-diffusion closure with different f(Ri) for stable and unstable layers K-diffusion closure with different f(Ri) for stable and unstable layers ED/MF (K-profile + M flux)

29
**Reduced Diffusion above Surface Layer**

1.0 0.8 0.6 0.4 0.2 10 Monin-Obukhov (new) LTG mom LTG heat LTG (old) 8 MO mom MO heat 6 f(Ri) Height [km] 4 LTG (old & new) 2 0.5 1.0 1.5 50 100 150 Richardson Number Ri Turbulent Length Scale l [m] Old large diffusion coefficients: Louis-Tiedtke-Geleyn (1982) empirical New small diffusion coefficients: Monin-Obukhov (1954) based on observations

30
**Z500 Activity increase due to K reduction**

K reduced control FC Activity: wave number 0-3 AN Activity: wave number 0-3 Activity: wave number 4-14 RMS error 115 T399 runs

31
**Shear power spectrum: resolution dependence**

10 100 1000 1 10-2 10-4 10-6 Spectral Shear Power Horizontal Wave Number 20 200 2000 T1279 T799 T399 T159 T2047 k-1.03 z=1000m Model lacks shear power near truncation. Flat spectrum suggests large missing shear at small scales.

32
**511 Forecasts ...even colder 2m T ...so basically the errors increase**

2T error CTL – analysis , 72 h FC, 0 UTC 2T difference SFMO – CTL , 72 h FC, 0 UTC ...even colder 2m T 2T error CTL – error SFMO , 72 h FC, 0 UTC ...so basically the errors increase

33
**Wind turning difference SFMO – CTL , 72 h FC, 0 UTC**

...but better wind turning... Wind turning difference SFMO – CTL , 72 h FC, 0 UTC

Similar presentations

OK

Mesoscale Modeling with a 3D Turbulence Scheme Jocelyn Mailhot and Yufei Zhu (Claude Pelletier) Environment Canada MSC / MRB 3 rd Annual Meeting on CRTI.

Mesoscale Modeling with a 3D Turbulence Scheme Jocelyn Mailhot and Yufei Zhu (Claude Pelletier) Environment Canada MSC / MRB 3 rd Annual Meeting on CRTI.

© 2018 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google