1. 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

2. 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

3. training course: boundary layer IV Parametrization above the surface layer (overview) Type of parametrizationApplication Geostrophic drag lawsModels with very low vertical resolution (used very little) Slab (integral) models Models that treat top of the boundary as surface Inversion restoring methodsMethod to enhance resolution near inversions K-closureModels with fair resolution K-profile closureModels with fair resolution TKE-closure Models with high resolution

4. 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

5. 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 Mixed layer model of the day-time boundary layer is a well- known example of integral model.

6. training course: boundary layer IV Mixed layer (slab) model of day time BL This set of equations is not closed. A closure assumption is needed for entrainment velocity or for entrainment flux.

7. 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: C E is entrainment constant (0.2) C s represents shear effects (2.5-5) but is often not considered

8. 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

9. training course: boundary layer IV Grid point models with 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. training course: boundary layer IV Diffusion coefficients according to MO-similarity Use relation between and to solve for

11. training course: boundary layer IV Louis formulation is equivalent to with 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. training course: boundary layer IV Stability functions F M,H based on Louis are very different from observational based (MO) (universal) functions. Louis’ functions provided larger exchanges for stable layers unstable stable

13. training course: boundary layer IV Geostrophic drag law derived from single column simulations. Observations are from Wangara experiment. Geostrophic drag law MO-based F M,H give more realistic drag law, with less friction (A) and a larger ageostrophic angle (B) More drag Larger ageos. angle

14. training course: boundary layer IV Single column simulations of stable BL FmFm FhFh LTG Revised LTG MO Revised LTG LTG MO 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.

15. 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 F H

16. training course: boundary layer IV Stable BL diffusion Relaxation integration Jan 96; 2m T-diff.: Revised LTG - control

17. 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

18. 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

19. training course: boundary layer IV K-profile closure Troen and Mahrt (1986) Heat flux h Profile of diffusion coefficients: Find inversion by parcel lifting with T-excess: such that: See also Vogelezang and Holtslag (1996, BLM, 81, 245-269) for the BL-height formulation.

20. training course: boundary layer IV K-profile closure (ECMWF implementation) Moisture flux Entrainment fluxes Heat flux zizi ECMWF entrainment formulation: ECMWFTroen/Mahrt C 1 0.6 0.6 D 2.0 6.5 C E 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.

21. 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 12 K m /(kzu*) 0 Diffusion coefficients Profiles of:

22. 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)

23. 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

24. 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

25. 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.

26. 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

27. training course: boundary layer IV TKE closure Eddy diffusivity approach: With diffusion coefficients related to kinetic energy:

28. training course: boundary layer IV 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.

29. training course: boundary layer IV 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. Best to implement TKE on half levels.