1. 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
training course: boundary layer; surface layer

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

3. 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:
Lowest model level
T1,q1 z1
Ts, qs
Surface
Ocean boundary condition
Land boundary condition
training course: boundary layer; surface layer

4. 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
training course: boundary layer; surface layer

5. Surface layer similarity (Monin Obukhov similarity)
Flux profile
For z/h << 1 flux is approximately equal to surface flux.
Considerations about the nature of the process:
z/zo >> 1
distance to surface determines turbulence length scale
shear scales with surface friction rather than with zo
Scaling parameters:
training course: boundary layer; surface layer

6. MO similarity for gradients
is a universal function of
dimensionless shear
Stability parameter
is a universal function of
dimensionless potential temperature gradient
Stability parameter
Note that with
we obtain:
training course: boundary layer; surface layer

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

8. 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
training course: boundary layer; surface layer

9. 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.
training course: boundary layer; surface layer

10. 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.
training course: boundary layer; surface layer

11. MO wind profile functions applied to observations
Unstable
Stable
training course: boundary layer; surface layer

12. Transfer coefficients
Surface fluxes can be written explicitly as:
U1,V1,T1,q1
Lowest model level
Surface
0, 0, Ts, qs z1
training course: boundary layer; surface layer

13. 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.
training course: boundary layer; surface layer

14. training course: boundary layer; surface layer
Louis scheme
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.
training course: boundary layer; surface layer

15. Stability functions for surface layer
unstable
stable
Land
Louis et al (dash)
MO-functions (solid)
Sea
training course: boundary layer; surface layer

16. 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 over sea and 0.01 over land, mainly due to surface roughness.
training course: boundary layer; surface layer

17. 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
training course: boundary layer; surface layer

18. Surface roughness length (definition)
Example for wind:
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 1
0.1
0.01
Often displacement height is used to obtain U=0 for z=0: U
Roughness lengths for momentum, heat and moisture are not the same.
Roughness lengths are surface properties.
training course: boundary layer; surface layer

19. Roughness length over land
Geographical fields based on land use tables:
Ice surface m
Short grass
0.01 m
Long grass
0.05 m
Pasture
0.20 m
Suburban housing
0.6 m
Forest, cities
1-5 m
training course: boundary layer; surface layer

20. 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.
Drag is determined by “silhouette area” per unit surface area. U
Effective roughness length:
training course: boundary layer; surface layer

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

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

23. 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.
training course: boundary layer; surface layer

24. 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
training course: boundary layer; surface layer

25. 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.
training course: boundary layer; surface layer

26. Transfer coefficents for moisture (10 m reference level)
CEN Neutral exchange coeff for evaporation
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
training course: boundary layer; surface layer

27. Low wind speeds and the limit of free convection
At zero wind speed, coupling with the surface disappears e.g.
for evaporation:
Lowest model level
U1,V1,T1,q1 z1
0 qs
Surface
Extension of MO similarity with free convection velocity:
inversion h
Surface
training course: boundary layer; surface layer

28. Air-sea coupling at low winds
Revised scheme: Larger coupling at low wind speed (0-5 ms-1)
Improved scheme: w_* + (Psi vs. F_M) + (z_0m=C_ch+niu/u_*) + (z_0h,q=niu/u_*)
training course: boundary layer; surface layer

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

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

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

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

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

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

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

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

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

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

39. BL budget considerations: IMET-stratus
Heat budget:
W/m2
Moisture budget:
mm/day
training course: boundary layer; surface layer