Parametrization of surface fluxes: Outline

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

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

Why is the finite difference formulation in the surface layer different from the other layers? φ2 model level 2 F1.5 Flux level 1.5 φ1 model level 1 F0 φs Surface 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

Fluxes are expressed in differences over the surface layer with help of transfer coefficients Lowest model level U1, V1, θ1,q1 z1 0, 0, θs, qs Surface • Transfer coefficients can be expressed in: • A surface characteristic (roughness lengths) • Stability effects • This can be done on the basis of Monin-Obukhov similarity. training course: boundary layer; surface layer

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

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

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

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

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

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

Roughness length over land Geographical fields based on land use tables: training course: boundary layer; surface layer

Roughness length over land (orographic contribution) Drag is determined by “silhouette area” per unit surface area. U Effective roughness length: • 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. Mason 1988, QJRMS, 114, 399-420 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

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

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

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 Beljaars 1995, 121, 255-270. training course: boundary layer; surface layer

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

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

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

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

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

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

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

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

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

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

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

Parametrization of surface fluxes: Outline