Parametrization of PBL outer layer Irina Sandu

1. Parametrization of PBL outer layer Irina Sandu • 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)

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. An example: Mixed layer (bulk) model of day time BL Bulk - Slab - Integral - Mixed Layer Models energy mass inversion entrainment This set of equations is not closed. A closure assumption is needed for entrainment velocity or for entrainment flux.

6. Closure for mixed layer model 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 The closure is based on the turbulent kinetic energy budget of the mixed layer:

7. 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

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

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

10. Stable boundary layer in the IFS: current problems SFMO 1/l=1/kz+1/λ , λ=150m since 36R4 Surface layer – SFMO Above: f = α* fLTG + (1- α) * fMO α = exp(-H/150) SFMO As in other NWP models the diffusion maintained in stable conditions is stronger than what LES or observations indicate

11. Stable boundary layer in the IFS: current problems 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 80 m 10 m 2011 OPERATIONAL Time (UTC)

12. 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

13. Impact of reducing the diffusion in stable conditions BAD GOOD Bias (FC-AN) T2m CTL ST-CTL ST: long tails short tails LT30: λ=150m λ=30m LT30-CTL

14. K-closure with local stability dependence (summary) flux • 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)!

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. ED/MF framework a M 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) h Heat flux Profile of diffusion coefficients: Find inversion by parcel lifting with T-excess: 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 ECMWF entrainment formulation: ECMWF Troen/Mahrt C1 0.6 0.6 D 2.0 6.5 CE 0.2 -

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)