Tephigrams

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Tephigrams

• ENVI1400 Lecture 8

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• Tephigrams are thermodynamic diagrams one of a
  range of such diagrams developed to help in the
  visual analysis of atmospheric profiles.
• They have the property that equal areas on the
  diagram represent equal amounts of energy.

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Tephigram Thermodynamic diagram showing the
vertical structure of the atmosphere.
Temperature (C)
Dewpointtemperature (C)
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Temperature (C)
Pressure (mb)
PotentialTemperature (C)or dry adiabat
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Saturationmixing ratio (g kg-1)
Saturated Adiabat
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Potential Temperature

• Much of the change in air temperature with
  altitude is due purely to the reduction in
  pressure.
• It is often easier to work with a measure of
  temperature that accounts for this
  pressure-related change in T, allowing us to
  focus on real differences in the energy content
  of the gas. The Potential Temperature is one such
  measure.

• Potential temperature, ? (K) is defined as the
  temperature a parcel of air would have if moved
  adiabatically to a pressure level of 1000 mb.
• R/Cp 0.286 for air
• T must be in Kelvin

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Adiabatic Lifting

• As a parcel of air is lifted, the pressure
  decreases the parcel expands and cools at the
  dry adiabatic lapse rate.
• As the parcel cools, the saturation mixing ratio
  decreases when it equals the actual water vapour
  mixing ratio the parcel becomes saturated and
  condensation can occur.
• The level at which saturation occurs is called
  the lifting condensation level.

Saturation mixing ratioequal to actual
watervapour mixing ratio of parcel
Liftingcondensationlevel
Dew pointat surface
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• If the parcel continues to rise, it will cool
  further the saturation mixing ratio decreases,
  and more water condenses out.
• Condensation releases latent heat this offsets
  some of the cooling due to lifting so that the
  saturated air parcel cools at a lower rate than
  dry air.
• The saturated (or wet) adiabatic lapse rate is
  NOT constant, but depends upon both the
  temperature and pressure.

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Stability

• If adiabatic ascent of a parcel of air results in
  a temperature less than the environmental
  temperature at any given level, then the air
  parcel will be more dense than the surrounding
  air, and will fall back towards its original
  level.
• Such conditions are described as (statically)
  stable. Similarly a parcel forced downward, under
  stable conditions will warm adiabatically to a
  temperature greater than the surrounding air,
  will be less dense, and will rise back towards
  its original level.

EnvironmentalLapse Rate
Dry adiabaticascent of surfaceair parcel
Environment warmerthan lifted parcel? stable
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EnvironmentalLapse Rate
Dry AdiabaticLapse Rate
Lifted air is warmerthan environment? unstable
If adiabatically lifted air is warmer than the
surrounding environment, it will be less dense,
and therefore buoyant, and will continue to rise.
Such conditions are described as statically
unstable, or convective. This is common near the
surface when heated by sunlight.
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Theoretical maximumaltitude to which parcelmay
overshoot
Equal areas
Equal areas on a tephigram represent equal
amounts of energy. The buoyant potential energy
available is represented by the area between the
environmental temperature curve and the adiabatic
lapse rate. As the parcel rises, this is
converted to kinetic energy. The rising parcel
may overshoot its level of neutral buoyancy by an
amount that just uses up all the kinetic energy.
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Absolute Stability

• Adiabatic lifting (dry wet) never results in
  the air temperature exceeding that of the
  environment. Lifting can only take place if
  forced, and at the expense of using energy. This
  is sometimes called forced convection and may
  occur due to mechanical mixing of stable air in
  strong winds.
• Cloud is formed if air lifted above the lifting
  condensation level (LCL), but remains limited to
  extent of parcel lifted from below.

stable
LCL
Temperature at surface Dew point at surface
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Absolute Instability

• Any adiabatic lifting results in air that is
  warmer than its environment, and thus in buoyant
  convection. The buoyancy force increases at the
  lifting condensation level due warming by the
  release of latent heat.
• Strong solar heating of the surface, or advection
  over a warmer surface often results in unstable,
  or convective, conditions in the boundary layer.
  Cumulus clouds frequently form in such conditions.

Cloud overshoots level of neutral stability
stable
unstable
LCL
Temperature at surface Dew point at surface
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Conditional Instability

• Forced adiabatic lifting of an air parcel through
  a region of static stability such that wet
  adiabatic lifting succeeds in raising the
  temperature above the environmental temperature.
  At this point, the parcel becomes convectively
  unstable and continues to lift under its own
  buoyancy.

stable
unstable
stable
LCL
Temperature at surface Dew point at surface
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Convective Instability

• The column of air A-B has a lapse rate less than
  the dry adiabatic lapse rate, and is thus stable.
• If the column is forced to lift adiabatically,
  the whole column cools. If the lower part of the
  column reaches saturation A', it starts to cool
  at the wet adiabatic lapse rate if this is less
  than the lapse rate of the column A'-B, the
  column becomes unstable.
• This type of instability may occur during large
  scale lifting up frontal surfaces or flow over
  mountain ranges.

B'
B
A'
A
LCL
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