Parametrization of surface fluxes: Outline

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Parametrization of surface fluxes Outline

• 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

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Parametrization of surface fluxes Outline

• 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

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Recap of Monin Obukhov similarity

• MO similarity

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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.
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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.
Surface flux parametrization is sensitive because
of large gradients near the surface.
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Transfer coefficients
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Numerical procedure The Richardson number

• This relation can be solved
• Iteratively
• Approximated with empirical functions
• Tabulated.

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Louis scheme
The older Louis formulation uses
With neutral transfer coefficient
And empirical stability functions for
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Stability functions for surface layer
unstable
stable
Land
Louis et al (dash) MO-functions (solid)
Sea
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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.

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Parametrization of surface fluxes Outline

• 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

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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.

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1
0.1
0.01
U

• Roughness lengths for momentum, heat and
  moisture are not the same.
• Roughness lengths are surface properties.

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Roughness length over land
Geographical fields based on land use tables
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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.

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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)
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Parametrization of flux divergence with
continuous orographic spectrum
Assume
1000 m
100 m
Write flux divergence as
Beljaars, Brown and Wood, 2003
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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.

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Parametrization of surface fluxes Outline

• 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

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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.
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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

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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
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Air-sea coupling at low winds
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Air-sea coupling at low winds (control)
Precipitation, JJA old formulation
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Air-sea coupling at low winds (revised scheme)
Precipitation, JJA new formulation
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Air-sea coupling at low winds
Near surface Theta_e difference New-Old
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Air-sea coupling at low winds
Theta and Theta_e profiles over warm pool with
old an new formulation
new
new
old
old
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Air-sea coupling at low winds
Zonal mean wind errors for DJF
Old
New