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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.

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Presentation on theme: "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."— Presentation transcript:

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) ParametrizationApplicationOrder and Type of Closure Bulk modelsModels that treat PBL top as surface0 th order non-local K-diffusion Models with fair resolution1 st order local Mass-flux Models with fair resolution1 st order non-local ED/MF (K& M)Models with fair resolution1 st order non-local K-profileModels with fair resolution1 st order non-local TKE-closureModels with high resolution1.5 th order non- local Higher order closureModels with high resolution2 nd or 3 rd 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 This set of equations is not closed. A closure assumption is needed for entrainment velocity or for entrainment flux. energy mass inversion entrainment

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

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 91-level model 31-level model Levels in ECMWF model K-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).

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

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

12 GABLS 3. Impact of the stability functions T2M hours since 12 UTC U200m U10m

13 GABLS 3 : Impact of the mixing length T2M hours since 12 UTC U200m U10m

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

17 ED/MF framework a M M-fluxenv. fluxsub-core flux Siebesma & Cuijpers, 1995

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

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: such that:

21 K-profile closure (ECMWF up to 2005) Moisture flux Entrainment fluxes Heat flux h ECMWF entrainment formulation: ECMWFTroen/Mahrt C D C E 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.

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 BuoyancyShear productionStorage Closure of TKE equation TKE from prognostic equation: 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. Turbulent transport Dissipation Pressure correlation

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 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 f(Ri) Richardson Number Ri LTG mom LTG heat MO mom MO heat LTG (old & new) LTG (old) Monin-Obukhov (new) Height [km] 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 FC Activity: wave number T399 runs RMS error K reduced control AN Activity: wave number 0-3 Activity: wave number 4-14

31 Shear power spectrum: resolution dependence Spectral Shear Power Horizontal Wave Number T1279 T799 T399 T159 T2047 k Model lacks shear power near truncation. Flat spectrum suggests large missing shear at small scales. z=1000m

32 511 Forecasts 2T error CTL – analysis, 72 h FC, 0 UTC2T difference SFMO – CTL, 72 h FC, 0 UTC 2T error CTL – error SFMO, 72 h FC, 0 UTC...so basically the errors increase...even colder 2m T

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


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