L14 Physics of dry air and moist air

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L14 Physics of dry air and moist air

• Potential temperature
• Pseudo-adiabatic charts
• Skew T ln p charts
• Moist air
• Saturated adiabatic lapse rate
• Normands Rule Cloud base

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Potential Temperature (?)

• The potential temperature of an air parcel is its
  temperature when compressed (or expanded)
  adiabatically to surface pressure (p0) (defined
  as a standard pressure of 1000 hPa).
• Again, start from the 1st Law of Thermodynamics,
  and make dq0

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Ideal Gas Law (see Lecture 8)
so
R is the specific gas constant for air R 287 J
kg-1 K-1
substitute in a
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Divide by RT
Integrate both sides, from the starting (p,T)
tothe surface (p0,T0), noting cp/R is a constant
Remember integral of 1/x is the natural log of x
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Integrating
Remember
Hence
or
Rearrange to give potential temperature, ?
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Happily, we can look at this graphicallye.g.,
the Pseudo-adiabatic chart
Re-arrange

• So if you plot p0.286 on y-axis,T on x-axis
• For a constant ?, (p00.286/?) is also a constant,
  so the graph yields a straight line with gradient
  given by (p00.286/?), and passing through T0 and
  p0

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Pseudo-adiabatic chart
y-axis is linear for p0.286 also linear for ln(p)

• Useful as now we can follow each line and
  determine graphically temperature at any
  pressure, assuming adiabatic expansion/compression

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Pseudo-adiabatic chart
Earths atmosphere

• Solves Poissons equation graphically!
• Disadvantage
• Everything happens in small region of the chart
• This can be overcome by skewing the temperature
  lines rather than plotting them straight up ?
  The Skew T-ln p chart

Earths atmosphere is never here
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Skew T-ln pchartdifference to
pseudo-adiabatic ln(p) rather than p0.286T
skewed

• Examples
• Kuching in Malaysia
• Valentia in Ireland.

Vertical T
Skew T
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What are all the lines on the skew T-ln p
chart?
isobar
isotherm
dryadiabat
saturated adiabat
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Example airplane air

• If an airplane at 250hPa takes air in at
• -51oC and adjusts it to cabin pressure (850 hPa),
  does the air have to be
• Heated
• Cooled
• to be comfortable?

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Followthe dry adiabatto 850 hPa
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Moist air

• See L6 Humidity
• Air contains some H2O molecules (water vapour)
• Vapour pressure (e) partial pressure exerted by
  the gaseous water (hPa)
• Mixing ratio (w) mass of water vapour / mass of
  dry air
• Warmer air can accommodate more water molecules
  the maximum for a given temperature is when the
  air is saturated
• For a given temperature, there is asaturation
  vapour pressure (es)saturation mixing ratio (ws)
• An air parcel can become saturated, e.g. by
  ascent and cooling
• Once saturated, further cooling will result in
  condensation of liquid water i.e. cloud droplets

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evaporation
condensation
Mixing ratio w mvapour/mdry normally given
units g/kg At saturation evaporation balances
condensation Saturation mixing ratio ws 0.622
es / p Relative Humidity w/ws x 100 e/es x
100
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Thermodynamics of saturated air

• As long as air remains unsaturated, it will
  behave like dry air
• However, once saturated, the condensation of
  liquid water releases latent heat
• This means that an ascending air parcel that
  becomes saturated will cool less than one that
  remains unsaturated
• We can theoretically derive how much the cooling
  is modified (not done here, see Wallace Hobbs
  p79-87 if interested), and define the Saturated
  Adiabatic Lapse Rate (SALR)
• The difference between the DALR and a SALR is
  largest for warmer air, as the water vapour
  content, and hence latent heat release are larger
• Saturated adiabats are solid green lines on the
  skew T-ln p chart

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Saturation mixing ratio
Derived Using ideal gas law, and def. of
saturation water vapour pressure (Clausius
Clapeyron, Dr Essery)?
Constant p w increases with T Constant T w
increases with decreasing p
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• Relative humidity RH 100e/es 100w/ws
• Dewpoint (Td) Temperature to which air must cool
  at constant pressure to be saturated
• Q Air at 1000 hPa and 18oC has a mixing ratio of
  6 g/kg. What is its relative humidity and
  dewpoint?

RH6/1310046 Dewpoint 6.5oC
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As unsaturated air lifts dry adiabatically, it
will eventually saturate Normands Rule
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This level is the lifting condensation level
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LCL Cloud base
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Lets look at some real data
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Albemarle, 00z Monday 17 Oct
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Albemarle, 00z Tuesday 18 Oct
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Summary

• Potential temperature the temperature of air
  compressed/expanded to 1000 hPa along a dry
  adiabat
• Pseudo-adiabatic charts graphically solve
  equations
• Skew T ln p charts will use in labs
• Moist air releases latent heat at saturation
  point
• Saturated adiabatic lapse rate less than DALR
  typically 6 K/km
• Normands Rule Can estimate cloud base height
  using surface temperature and moisture