Mixing and Convection Chapt 4 page 44'

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Mixing and ConvectionChapt 4 page 44.
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Case 1 no condensation
Specific humidity
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Heat lost by warm sample heat gained by cold
sample
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Case 2 condensation and mixing
Question can condensation occur during the
mixing of two unsaturated samples (isobaric
mixing)?
Yes, in the winter when you see your breath!
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Clausius-Clapeyron
e
es(T)
e2
e1
T1
T2
T
es gt ef so isobaric mixing in this case does NOT
result in condensation.
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e
es(T)
e2
e1
T1
T2
T
Isobaric mixing in this case will result in
condensation because es lt ef
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How does one determine if condensation will occur?

• 1. Determine T e that would result if NO
  condensation were to occur.
• 2. Compare e with es(T)
• if e lt es(T) - no condensation
• if e gt es(T) - condensation will occur

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If Condensation occurs, what is the final e T?

• e must be less than that calculated assuming no
  condensation because vapor will be removed.
• T must be greater because latent heat has been
  released.

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Latent Heat released during condensation
dq -Lvdw
Isobaric Process dq cpdT
Since w ee/p - Lvdw Lv ede/p cpdT
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e
es(T)
(e2 ,T2)
(e1 ,T1)
T
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To Determine the Final e T
Find the intersection of the isobaric
condensation equation with the Clausius-Clapeyron
equation using eT as initial conditions. The
isobaric condensation equation must be integrated
to arrive at an algebraic form
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The simplified form of the Clausius-Clapeyron equa
tion can be combined with the isobaric condensatio
n equation to find the final values of e and T.
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Since we can not find xo analytically, how
do we proceed?
Expand f and g in a Taylors series f(x)
f(x) f(x)(x- x) g(x) g(x)
g(x)(x- x) Neglect higher order terms and
solve for x.
Isnt this what we did for the CC equation?
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Adiabatic Mixing

• Parcels from different pressure levels are mixed
  after being brought together adiabatically.
• The final state of the combined parcel can be
  calculated as shown previously.
• When a column of air is thoroughly mixed, the
  specific humidity becomes constant throughout.

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Specific Humidity of a Mixed Parcel
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Convective Condensation Level
CCL Pressure and temperature at
which condensation occurs in/at top of a well
mixed layer. It can be found by the
intersection of the dry adiabat for the layer
with the mixing ratio isopleth for the layer.
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Lifting Condensation Level
LCL level at which condensation will occur if
a parcel is lifted from the surface in a
dry adiabatic process with constant w until
just saturated.
Note LCL CCL if the layer is well mixed.
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Fair Weather Cumulus Clouds Fair weather
cumulus are form atop buoyant bubbles of air
(thermals) that rise from Earth's surface. As
bubbles rise, the water vapor mixing ratio
remains constant but the temperature falls and
the relative humidity increases until it reaches
the saturation vapor pressure, 100 RH. Here
droplets condense and clouds form. This occurs
at the Lifting Condensation Level, (LCL) where
the flat cloud bases are seen.
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Fair Weather Cumulus
Fair weather cumulus 1 pm EST July 7, 2007, a
smoggy day
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Boundary Layer Venting Through Fair Weather
Cumulus (Cumulus Humilis)
H2SO4
H2SO4
Cumulus
Cumulus
Inversion
SO2
SO2
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Two Reservoir Model (Taubman et al., JAS, 2004)
H2SO4
cloud
cloud
SO2