Surface Exchange Processes

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Surface Exchange Processes

• SOEE3410 Lecture 3
• Ian Brooks

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Turbulence

• The exchange of energy and trace gases at the
  surface is achieved almost entirely via turbulent
  mixing.
• Wind is generated on large scales by spatial
  differences in atmospheric pressure (ultimately
  resulting from radiative heating/cooling)
• Kinetic energy of wind is dissipated at small
  scales by friction (and ultimately as heat)

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Sources of Turblence

• Friction mechanical generation of turbulence
• Flow over rough surface / obstacles
• Small perturbations of the flow act as obstacles
  to the surrounding flow
• Shear in the flow can result in instability
  overturning
• Turbulence results in a wind speed profile that
  is close to logarithmic

z
Wind speed
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• Convection
• heating of air near the surface (or cooling of
  air aloft) increases (decreases) its density with
  respect to the air around it, so that it becomes
  buoyant.

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Large Eddy Model simulation of convective mixing
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Turbulent Fluxes

• The turbulent flux of some quantity x (momentum,
  heat, CO2,) is defined as

Flux of x 1 (w'1x'1 w'2x'2 w'Nx'N)
N w'x' Where
w'N wN w And an overbar signifies an
average
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• For example, the wind stress at the surface (the
  vertical flux of horizontal momentum) is
• where ? is air density, and U the wind speed.
  More strictly it is
• where u is the wind component in the direction
  of the mean wind direction and v the component
  perpendicular to the mean wind.

• The wind stress is frequently represented by the
  friction velocity

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Flux Parameterizations

• Measurement of turbulent fluxes is possible only
  on small scales, using expensive instrumentation.
• Large-scale climate models do not include
  small-scale processes such as turbulence
  directly they must parameterize the effects of
  turbulence in terms of large-scale mean
  quantities
• Mean wind speed
• Temperature difference between surface and a
  given altitude
• Within the surface layer turbulent fluxes are
  almost constant with altitude

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z
U
U mean wind speed Z altitude k
von-Karmans constant (?0.4) zo the roughness
length a measure of the roughness of the
surface the altitude at which the mean wind
speed falls to zero. u the friction velocity
a measure of how variable (turbulent) the wind
speed is in the direction of the mean wind.
(w'u')½
Wind speed
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• Similar relationships describe the shape of
  vertical profiles of scalar quantities such as
  temperature, water vapour concentration, and gas
  concentrations. e.g
• Where Ts is the surface temperature and T is a
  measure of how variable the temperature is.

• The sensible heat flux, QH is given by
• where ? is the air density and Cp is the
  specific heat capacity of air at constant
  pressure.

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Bulk Transfer Schemes

• The vertical flux F? of any quantity, ?, is
  assumed to be driven by its vertical gradient,
  approximated by the difference in value between
  two levels usually the surface and z.
• Where UT represents a transport velocity.
• Note - sign direction of flux is down-gradient.

• The transport velocity is usually parameterized
  as a function of some measure of turbulence. e.g.
• Where Uz is the mean wind speed at height z, and
  CD is a bulk transfer coefficient.

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• Using u as a measure of the surface stress
  associated with drag
• For momentum transfer, CD is often called the
  drag coefficient.
• (Note, CD is dimensionless. It is defined for
  measurements at a specific height only)

• The fluxes of heat and moisture can be similarly
  parameterized
• CH and CE are the bulk transfer coefficients for
  heat and moisture. They are often assumed to be
  equal to CD, but this is not always a valid
  assumption.

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A note on sign conventions

• In meteorological applications fluxes are usually
  defined to be positive when directed upwards, so
  that a positive surface heat flux adds heat to
  the atmosphere.
• In oceanographic applications positive is often
  defined to be downwards, so a positive surface
  heat flux adds heat to the ocean.

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Sensible Heat Flux

• The flux of energy due to the movement of parcels
  of air at different temperatures.
• Results from difference in temperature between
  the surface and overlying air.
• Radiative warming or cooling of the surface
• Advection of air over a surface at different
  temperature

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Animation of monthly sensible heat flux (W/m2)
From http//geography.uoregon.edu/envchange/clim_a
nimations/index.html
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Latent Heat Flux

• The flux of energy associated with the latent
  heat of evaporation of water. Actually a flux of
  water vapour.
• Lv is the latent heat of vaporisation of water,
  q is the mass-mixing ratio of water vapour in
  air, ? is the air density.

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• While the sensible heat flux is dependent
  primarily on surface temperature, the latent heat
  flux depends in a much more complex fashion on
  surface type
• Rock, tarmac, etcsolid, non-porous surfaces a
  source of moisture only when surface water
  present
• Water surface ocean, lakes, etc
• Soils can draw water up from below surface soil
  colour affects solar heating evaporation
• Plant cover evapotranspiration from
  leavesdependent upon growing conditions, season,
  etc.

• Ice surface highly reflective, does not absorb
  much solar radiation. May be dry (T lt 0C) or wet
  (Tair ?? 0C). The surface energy balance over
  ice is not fully understood, and is strongly
  affected by melting/freezing while ice is
  present and T near 0C, heat exchange tends to
  result in phase change of water rather than a
  change in near-surface temperature.

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Animation of monthly latent heat flux (W/m2)
From http//geography.uoregon.edu/envchange/clim_a
nimations/index.html
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Effect of Surface Roughness

• Rougher surfaces generate more turbulence,
  increasing transfer rates across the surface.
• There are three processes contributing to the
  effective drag on the atmosphere
• Frictional skin drag related to molecular
  diffusion. Applies equally to momentum, heat,
  other scalars.
• Form drag related to the dynamic pressure
  difference resulting from the deceleration of air
  as flows around an obstacle. Applies only to
  momentum flux. The effect of form drag over small
  obstacles (grass, trees, etc) is usually
  incorporated with frictional drag into the bulk
  parameterization.
• Wave drag related to the transport of momentum
  by gravity waves in statically stable air e.g.
  mountain waves. Applies only to momentum

The additional drag processes applicable to
momentum suggest that there ought to be
differences between the drag coefficients for
momentum and scalar quantities!
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• On the small scale, surface roughness obviously
  depends upon the type of surface
• sand, grass, low shrubs, trees,
• The roughness length, zo, depends upon the
  surface type, but the relationship is complex
  it is not easy to specify the roughness length
  simply from a knowledge of the surface.
• Surface roughness values are estimated from
  measurements over different surface types, and
  specified for each surface grid point within
  numerical models.

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Some Typical Values

• Surface roughness
• Flat grassland 0.03 m
• Low crops 0.1 m
• High crops 0.25 m
• Parkland, bushes 0.5 m
• Forest, suburban 0.5 1.0 m
• Open ocean 0.0002 m

• Drag Coefficient CDN (10m)
• N. America 10.1 10-3
• S. America 26.6 10-3
• Northern Africa 2.7 10-3
• Europe 7.9 10-3
• Asia (north of 20ºN) 3.9 10-3
• Asia (south of 20ºN) 27.7 10-3

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Effect of Atmospheric Stability

• Unstable (convective) conditions enhance
  turbulence generation and promote mixing
• Fluxes increase
• Stable conditions suppress turbulence.
• Fluxes decrease
• In strongly stable conditions turbulence may
  cease completely and all turbulent fluxes reduce
  to zero.

• Bulk transfer coefficients are usually derived
  for neutral conditions and the bulk flux
  equations modified to include factors to account
  for stability effects.
• Accounting for stability effects greatly
  increases the complexity of the parameterizations.

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• Drag coefficient equation, including a stability
  correction

Where the stability correction for stable
conditions (z/L gt 0) is
and for unstable conditions (z/L lt 0) is
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Gas Fluxes

• CO2 fluxes over land are coupled closely to
  vegetation. CO2 diffuses into leaves via stomata,
  where some of it takes part in photosynthesis.
  55 returned to atmosphere without taking part
  in photosynthesis, 45 fixed by conversion to
  carbohydrates.
• For a biological system in equilibrium (no net
  gain/loss in biological mass), the same quantity
  of Carbon would be returned to the environment
  via decomposition, combustion, and processing by
  animals.