Tephigrams are thermodynamic diagrams that show the vertical structure of the atmosphere. They have the property that equal areas on the diagram represent equal amounts of energy. Tephigrams depict the temperature, dewpoint, potential temperature, and saturation mixing ratio to analyze atmospheric stability and potential for cloud formation and convection. Areas between environmental temperature curves and adiabatic lapse rates indicate the potential buoyant energy available for parcel lifting.

1. 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)
Dewpoint
temperature (°C)

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Temperature (°C)
Pressure (mb)
Potential
Temperature (°C)
or ‘dry adiabat’

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Saturated Adiabat Saturation
mixing ratio (g kg-1)

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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
Cp
R
P
T 






1000


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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.
Lifting
condensation
level
Saturation mixing ratio
equal to actual water
vapour mixing ratio of parcel
Dew point
at 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.
Environmental
Lapse Rate
Dry adiabatic
ascent of surface
air parcel
Environment warmer
than lifted parcel
 stable

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Lifted air is warmer
than environment
 unstable
Environmental
Lapse Rate
Dry Adiabatic
Lapse Rate
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 maximum
altitude to which parcel
may 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.
LCL
Temperature at surface
Dew point at surface
stable

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

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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.
LCL
Temperature at surface
Dew point at surface
unstable
stable
stable

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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.
A'
B
B'
A
LCL

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