Atmospheric Stability

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Atmospheric Stability Profile Methods

• Atmospheric stability It is the tendency of air
  to move by buoyant convective processes arising
  from density differences.
• There are two kinds of eddies
• 1) mechanically-generated eddies and
• 2) thermally generated eddies

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Oke (1987)
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• ?u/?z u/?zFm
• where Fm is the dimensionless stability
  correction for momentum.
• There are similar stability correction
  coefficients for heat, moisture, and mass (carbon
  dioxide) -- FH, Fv, Fc, so that
• the gradient equations for these quantities would
  be (see notes)

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• The stability corrected eddy diffusivity is K
  ?2z2 ?u/?z Fm-1
• and the logarithmic wind profile equation is u
  u/? ln(z/z0) Fm
• The stability corrected aerodynamic flux
  equations can now finally be written (see notes)

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Oke (1987)
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• A convenient measure of atmospheric stability and
  the state of turbulence in the lowest layers is
  the (gradient form of the) Richardson Number Ri
• Ri g/? (??/?z) / (?u/?z)2
• where g is acceleration due to gravity (9.8 m
  s-2), ? is mean (potential) temperature in the
  layer ?z.
• Ri will be positive when the air is stable, and
  negative when the air is unstable.

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• Since (?u/?z) increases towards the surface, Ri
  decreases towards the surface.
• Thus buoyancy becomes less important with respect
  to mechanical turbulence near the surface.
• At Richardson numbers less than about -0.25
  (referred to as the critical Richardson Number),
  the atmosphere will be turbulent in nature.
• When Ri gt -0.25, turbulence will tend to be
  suppressed by a stable stratification in the
  atmosphere.

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• Empirical relationships have been found between
  the Richardson number and the stability
  corrections according to the following scheme
• Stable case (Ri positive) (Fm Fx)-1 (1 - 5
  Ri)2
• Unstable case (Ri negative) (Fm Fx)-1 (1 - 16
  Ri)3/4
• where Fx is the stability function for the
  property being transferred (momentum, heat,
  moisture, or mass).
• Observations suggest that Fh FV FC Fm in
  moderately stable conditions, but Fh FV FC
  Fm2 in unstable conditions.

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Oke (1987)
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Bowen ratio energy balance method

• This method requires similarity between KH, KV,
  but not with KM and so is not stability limited
  since
• KH/KV Fh / FV
• if Fh FV, then for all stability regimes KH
  KV.
• The Bowen ratio (ß) is defined as the ratio of QH
  / QE.

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• ß QH / QE Ca ?T/Lv ??v
• So that the surface energy balance can be
  written
• QH ß(Q - QG)/(1 ß)
• QE (Q - QG)/(1 ß)
• So that to evaluate QH and QE, all that is needed
  is Q (net pyranometer), QG (soil heat flux
  plate), and ß from temperature and humidity
  differences over the same height interval.