1. training course: boundary layer; surface layer Parametrization of surface fluxes: Outline Surface layer (Monin Obukhov) similarity Surface fluxes: Alternative formulations Roughness length over land –Definition –Orographic contribution –Roughness lengths for heat and moisture Ocean surface fluxes –Roughness lengths and transfer coefficients –Low wind speeds and the limit of free convection –Air-sea coupling at low wind speeds: Impact

2. training course: boundary layer; surface layer Mixing across steep gradients Stable BLDry mixed layerCloudy BL Surface flux parametrization is sensitive because of large gradients near the surface.

3. training course: boundary layer; surface layer Why is the finite difference formulation in the surface layer different from the other layers? model level 1 Surface φ 2 model level 2 Flux level 1.5 F 1.5 F 0 φ 1 φ s

4. training course: boundary layer; surface layer Boundary conditions for T and q have different character over land and ocean Surface fluxes of heat and moisture are proportional to temperature and moisture differences: T 1,q 1 Lowest model level Surface T s, q s z1z1 Ocean boundary conditionLand boundary condition

5. training course: boundary layer; surface layer Fluxes are expressed in differences over the surface layer with help of transfer coefficients U 1, V 1, θ 1,q 1 Lowest model level Surface 0, 0, θ s, q s z1z1 Transfer coefficients can be expressed in: A surface characteristic (roughness lengths) Stability effects This can be done on the basis of Monin-Obukhov similarity.

6. training course: boundary layer; surface layer For z/h << 1 fluxes are approximately equal to surface flux. In MO theory the following parameters are usually defined: Surface layer similarity (Monin Obukhov similarity) The relevant scaling parameters are: Surface heat flux Surface momentum flux Height above the surface Flux profile

7. training course: boundary layer; surface layer MO similarity for gradients dimensionless shearStability parameter dimensionless potential temperature gradient Stability parameter is a universal function of Note that withwe obtain:

8. training course: boundary layer; surface layer Observations of as a function of z/L, with Empirical gradient functions to describe these observations: stableunstable MO gradient functions

9. training course: boundary layer; surface layer Integral profile functions for momentum Dimensionless wind gradient (shear) or temperature gradient functions can be integrated to profile functions: with: integration constant (roughness length for momentum) wind profile function, related to gradient function: Profile functions for temperature and moisture can be obtained in similar way.

10. training course: boundary layer; surface layer Integral profile functions: Momentum, heat and moisture Profile functions for surface layer applied between surface and lowest model level provide link between fluxes and wind, temperature and moisture differences.

11. training course: boundary layer; surface layer MO wind profile functions applied to observations Stable Unstable Holtslag 1984, BLM, 29, 225-250

12. training course: boundary layer; surface layer Transfer coefficients Surface fluxes can be written explicitly as: U 1,V 1,T 1,q 1 Lowest model level Surface 0, 0, T s, q s z1z1

13. training course: boundary layer; surface layer Numerical procedure: The Richardson number The expressions for surface fluxes are implicit i.e they contain the Obukhov length which depends on fluxes. The stability parameter z/L can be computed from the bulk Richardson number by solving the following relation: This relation can be solved: Iteratively; Approximated with empirical functions; Tabulated.

14. training course: boundary layer; surface layer Louis scheme (alternative formulation) The older Louis formulation uses: With neutral transfer coefficient: And empirical stability functions for Initially, the empirical stability functions,, were not related to the (observed-based) Monin-Obukhov functions. Louis 1979, BLM, 17, 187-202

15. training course: boundary layer; surface layer Stability functions for surface layer Louis et al (dash) MO-functions (solid) unstablestable Land Sea Louis et al. 1982, ECMWF workshop

16. training course: boundary layer; surface layer Surface fluxes: Summary MO-similarity provides solid basis for parametrization of surface fluxes: Different implementations are possible (z/L-functions, or Ri- functions) Surface roughness lengths are crucial aspect of formulation. Transfer coefficients are typically 0.001 over sea and 0.01 over land, mainly due to surface roughness.

17. training course: boundary layer; surface layer Parametrization of surface fluxes: Outline Surface layer (Monin Obukhov) similarity Surface fluxes: Alternative formulations Roughness length over land –Definition –Orographic contribution –Roughness lengths for heat and moisture Ocean surface fluxes –Roughness lengths and transfer coefficients –Low wind speeds and the limit of free convection –Air-sea coupling at low wind speeds: Impact

18. training course: boundary layer; surface layer Surface roughness length (definition) Surface roughness length is defined on the basis of logarithmic profile. For z/L small, profiles are logarithmic. Roughness length is defined by intersection with ordinate. 10 0.1 0.01 1 U Example for wind: Often displacement height is used to obtain U=0 for z=0: Roughness lengths for momentum, heat and moisture are not the same. Roughness lengths are surface properties.

19. training course: boundary layer; surface layer Roughness length over land Geographical fields based on land use tables: Ice surface0.0001 m Short grass0.01 m Long grass0.05 m Pasture0.20 m Suburban housing0.6 m Forest, cities1-5 m

20. training course: boundary layer; surface layer Roughness length over land (orographic contribution) Small scale sub-grid orography contributes substantially to surface drag due to pressure forces on orographic features (form drag). Effects are usually parametrized through orographic enhancement of surface roughness. Effective roughness length: Drag is determined bysilhouette area per unit surface area. U Mason 1988, QJRMS, 114, 399-420

21. training course: boundary layer; surface layer Orographic form drag (simplified Wood and Mason, 1993): Shape parameters Drag coefficient Silhouette slope Wind speed Reference height Vertical distribution (Wood et al, 2001): Roughness length over land (orographic contribution)

22. training course: boundary layer; surface layer Assume: Write flux divergence as: Parametrization of flux divergence with continuous orographic spectrum: 100 m 1000 m Beljaars, Brown and Wood, 2003

23. training course: boundary layer; surface layer Roughness lengths for heat and moisture Roughness lengths for heat and moisture are different from the aerodynamic roughness length, because pressure transfer (form drag) does not exist for scalars. Vegetation: roughness lengths for heat and moisture are ~ 10x smaller than aerodynamic roughness.

24. training course: boundary layer; surface layer Parametrization of surface fluxes: Outline Surface layer (Monin Obukhov) similarity Surface fluxes: Alternative formulations Roughness length over land –Definition –Orographic contribution –Roughness lengths for heat and moisture Ocean surface fluxes –Roughness lengths and transfer coefficients –Low wind speeds and the limit of free convection –Air-sea coupling at low wind speeds: Impact

25. training course: boundary layer; surface layer Roughness lengths over the ocean Roughness lengths are determined by molecular diffusion and ocean wave interaction e.g. Current version of ECMWF model uses an ocean wave model to provide sea-state dependent Charnock parameter.

26. training course: boundary layer; surface layer Transfer coefficents for moisture (10 m reference level) Using the same roughness length for momentum and moisture gives an overestimate of transfer coefficients at high wind speed The viscosity component increases the transfer at low wind speed C EN Neutral exchange coeff for evaporation

27. training course: boundary layer; surface layer Low wind speeds and the limit of free convection At zero wind speed, coupling with the surface disappears e.g. for evaporation: U 1,V 1,T 1,q 1 Lowest model level Surface 0 q s z1z1 Surface h inversion Extension of MO similarity with free convection velocity: Beljaars 1995, 121, 255-270.

28. Miller et al. 1992, J. Clim., 5, 418-434. Air-sea coupling at low winds Revised scheme: Larger coupling at low wind speed (0-5 ms -1 )

29. training course: boundary layer; surface layer Air-sea coupling at low winds (control) Precipitation, JJA; old formulation

30. training course: boundary layer; surface layer Air-sea coupling at low winds (revised scheme) Precipitation, JJA; new formulation

31. training course: boundary layer; surface layer Air-sea coupling at low winds Near surface Theta_e difference: New-Old

32. training course: boundary layer; surface layer Air-sea coupling at low winds Theta and Theta_e profiles over warm pool with old an new formulation new old new old

33. training course: boundary layer; surface layer Air-sea coupling at low winds Zonal mean wind errors for DJF Old New

34. training course: boundary layer; surface layer IMET-stratus buoy / ECMWF (20 S 85 W) Latent heat flux

35. training course: boundary layer; surface layer IMET-stratus buoy vs. ECMWF (20 S 85 W) Sensible heat flux

36. training course: boundary layer; surface layer IMET-stratus buoy vs. ECMWF (20 S 85 W) Horizontal wind speed

37. training course: boundary layer; surface layer IMET-stratus buoy vs. ECMWF (20 S 85 W) Water/air q- difference

38. training course: boundary layer; surface layer IMET-stratus buoy vs. ECMWF (20 S 85 W) Water/air T-difference

39. training course: boundary layer; surface layer BL budget considerations: IMET-stratus -3+3.3-0.3 mm/day +40+10 -80 +20 +10 W/m2 Moisture budget: Heat budget: